I disagree that Captain Hook could ever not be a villain.
Most people have an innate sense of right and wrong and can easily tell when someone else is doing something obviously bad to them, and less easily tell when they are doing something obviusly bad to someone else. And of course when the evil that they do is not so obvious but requires some thought to realize that innate sense doesn't work so well.
So good and evil are not relative. Being better than someone else doesn't make someone good; to be good someone has to pass the minimum standards for goodness, even if they are many times better than the more evil persons around them.
So Peter Pan can be interpreted as being evil, and so one of the villains in Peter Pan, without making every other character better than they are; without making them good enough to not be villains.
Captain Hook was a pirate. All pirates are evil criminals and thus are villains in any stories they are in, even the stories which make them protagonists.
Piracy is robbery at sea, always with the threat of violence (makng terroristic threats) and often with actual violence (assault, murder, etc.). Such actions are crimes at sea as well as on land for good reasons. Piracy is not evil because it is illegal, it is illegal because it is evil.
Nautical trade has been an important part of the world's economy for millennia, and in recent centuries it has become more and more vital for civilization. Discouraging and interrupting that trade is bad for hte world as a whole.
Because of the vital importance of nautical trade to keep people alive, it is wrong and evil, though legal, when naval forces of a country sieze merchant ships of countries they are at war with and blockade their coasts. It is even more wrong and evil, though still legal in some countries, for a country to commission civilian privateers, undisciplined and more likely to commit atrocities for profit, to attack the merchant shipping of countries they are a war with. And it is more wrong and evil still, and totally illegal, for private individuals to become pirates and attack merchant ships of all countries.
If any changes should be made in those laws, it should be to forbid the use of privateers and navies to sieze enemy merchant ships and blockade coasts and make such practices as illegal as piracy is, not to make piracy as legal as those practices are now.
It is possible that some of the teenage pirates in history were young enough to not be legally guilty of piracy, and so might not have been evil. And I guess that John King and the boy captured with Nicholas Brigaut were young enough pirates to not be considered villains.
And it is possible to describe a fictional character as a pirate, and for characters to describe them as a pirate, without them committing any acts of piracy as far as the readers or audience can tell, and without giving much evidence that they commit acts of piracy offstage. Such a character fits the TV trope of "The Pirates Who Don't Do Anything":
But pirates who don't do anything are not really pirates, and I think that almost every single version of Peter Pan depicts Captain Hook and his crew behaving enough like real pirates to be considered evil. So Captain Hook is a villain.
And Hook has no justification for seeking revenge on Peter Pan for cutting off his hand. Instead Hook should have been grateful to Peter Pan for merely cutting off his hand and so treating Hook a lot better than he deserved.
Part One: Protagonists and Antagonists, Heroes and Villains.
Writers have two sets of terms for main characters:
Protagonist and antagonist, and hero and villain.
In the vast majority of stories, there is a least one protagonist, and sometimes several, who the story follows and who the audience usually wants to succeed in their goals. The obstacles the protagonists have to overcome usually include one or more characters called antagonists who oppose the efforts of the protagonists.
In fiction, a hero is someone who makes great efforts to achieve goals which are good, and often those goals are of great benefit to many other people. In fiction a villain is a character who makes efforts to achieve goals which are bad or even evil, and often those goals are very harmful to many other people.
It is possible to write a story without heroes and villains. Suppose their is story where a little child seeks to get a treat which their mother says they shouldn't get. A writer could make either the child or the mother the protagonist, thus making the other one the antagonist of the story. But it would take some very great writing to make the readers think that either character was a hero or a villain.
I note it is traditional in the stage version of Peter Pan Mr. Darling and Captain Hook are usually portrayed by the same actor, to show that both are antagonists. But obviously Mr. Darling isn't depicted as being evil enough to be a villain.
In works of fiction which have heroes and villains, the protagonists are usually the heroes and the antagonists are usually the villains. But that doesn't have to be the case.
Both the protagonist and the antagonist can be heroes. Both the protagonist and the Antagonist can be villains. The protagonist can be a hero and the antagonist can be a villain. The protagonist can be a villain and the antagonist can be a hero. And sometimes protagonists and/or antagonists are on the borderline between good and evil.
Part Two: An Example of Villain Protagonists and a Hero Antagonist.
For example, there is the Disney television movie The Computer Wore Tennis Shoes (1995), a loose remake of the 1969 move. In the 1995 version, Medfield College reaches a new low, taking their tradition of cheating in sports into academics. There is a TV program where college students compete to answer questions. A freak accident, possibly only in goofy movies, gives Medfield student Dexter Riley all the information on the internet.
So the dean of Medfield makes Dexter compete in the program and win games, giving the impression that Medfield has a good education system to increase enrollment. The dean tells Dexter that if he doesn't compete his slacker buddies will be expelled. At the rival Hale University, where 12-year-old Norwood Gills had been the reigning champion, the Dean schemes to get Dexter to come to Hale University.
Obviously Dexter and his friends are the protagonists, and the Deans of Medfield and of Hale, and two sinister government agents, and Norwood, are antagonists. But are there heroes and villains?
The two government agents are ruthless enough to throw Dexter out of the back of a moving vehicle, and never prove that they work for the US government.
The Dean of Medfield College wants to lie and claim that Medfield has a great educational system, tricking hundreds or thousands of persons into enrolling there at a cost of thousands of dollars each. So he wants to commit grand larceny and fraud. He pressures Dexter into becoming his accomplice in crime. The dean of Hale University has been using Norwood for similar fraudulent advertising and tries to use Dexter for similar deception.
So basically all of the protagonists and antagonists are villains - except for Norwood. Norwood tries to expose Dexter's fraud. He does that for selfish personal reasons but has to be aware that it will also prevent hundreds and thousands of people from being conned out of their money. So that makes Norwood a hero in my book. And during the short period of the story - such is Norwood's anger - he comes to understand how knowledge was implanted into Dexter's mind and how to implant knowledge and how to erase it - such is Norwood's genius.
So i say that little known tv movie is a great example of a story where all the protagonists and most of the antagonists are villains, and one of the antagonists is the hero.
When person A is originally described as the good guy and person B is originally described as the bad guy, and then someone tries to convince me that the opposite is true, they have an uphill battle to convince me. I am cynical enough that such an effort would usually only half succeed, so that I decide that the good guy was actually bad but not that the bad guy was actually good.
Thus such attempts to revise stories or history usually end up with me thinking that the conflict was between two different groups of bad guys.
Part Three: The Evidence for Hook's Villain Status in the novel Peter Pan
I found an online text of Peter Pan.
In "Chapter IV The Flight":
John said “How ripping,” but decided to have tea first. He asked if there were many pirates on the island just now, and Peter said he had never known so many.
“Who is captain now?”
“Hook,” answered Peter, and his face became very stern as he said that hated word.
Then indeed Michael began to cry, and even John could speak in gulps only, for they knew Hook’s reputation.
“He was Blackbeard’s bo’sun,” John whispered huskily. “He is the worst of them all. He is the only man of whom Barbecue was afraid.”
“That’s him,” said Peter.
The pirates are introduced in "Chapter V The Island Come True"
The boys vanish in the gloom, and after a pause, but not a long pause, for things go briskly on the island, come the pirates on their track. We hear them before they are seen, and it is always the same dreadful song:
“Avast belay, yo ho, heave to,
A-pirating we go,
And if we’re parted by a shot
We’re sure to meet below!”
So the pirates themselves admit that they are so evil they are damned.
A more villainous-looking lot never hung in a row on Execution dock. Here, a little in advance, ever and again with his head to the ground listening, his great arms bare, pieces of eight in his ears as ornaments, is the handsome Italian Cecco, who cut his name in letters of blood on the back of the governor of the prison at Gao. That gigantic black behind him has had many names since he dropped the one with which dusky mothers still terrify their children on the banks of the Guadjo-mo. Here is Bill Jukes, every inch of him tattooed, the same Bill Jukes who got six dozen on the Walrus from Flint before he would drop the bag of moidores; and Cookson, said to be Black Murphy’s brother (but this was never proved), and Gentleman Starkey, once an usher in a public school and still dainty in his ways of killing; and Skylights (Morgan’s Skylights); and the Irish bo’sun Smee, an oddly genial man who stabbed, so to speak, without offence, and was the only Non-conformist in Hook’s crew; and Noodler, whose hands were fixed on backwards; and Robt. Mullins and Alf Mason and many another ruffian long known and feared on the Spanish Main.
In the midst of them, the blackest and largest in that dark setting, reclined James Hook, or as he wrote himself, Jas. Hook, of whom it is said he was the only man that the Sea-Cook feared. He lay at his ease in a rough chariot drawn and propelled by his men, and instead of a right hand he had the iron hook with which ever and anon he encouraged them to increase their pace. As dogs this terrible man treated and addressed them, and as dogs they obeyed him. In person he was cadaverous and blackavized, and his hair was dressed in long curls, which at a little distance looked like black candles, and gave a singularly threatening expression to his handsome countenance. His eyes were of the blue of the forget-me-not, and of a profound melancholy, save when he was plunging his hook into you, at which time two red spots appeared in them and lit them up horribly. In manner, something of the grand seigneur still clung to him, so that he even ripped you up with an air, and I have been told that he was a raconteur of repute. He was never more sinister than when he was most polite, which is probably the truest test of breeding; and the elegance of his diction, even when he was swearing, no less than the distinction of his demeanour, showed him one of a different cast from his crew. A man of indomitable courage, it was said that the only thing he shied at was the sight of his own blood, which was thick and of an unusual colour. In dress he somewhat aped the attire associated with the name of Charles II, having heard it said in some earlier period of his career that he bore a strange resemblance to the ill-fated Stuarts; and in his mouth he had a holder of his own contrivance which enabled him to smoke two cigars at once. But undoubtedly the grimmest part of him was his iron claw.
Let us now kill a pirate, to show Hook’s method. Skylights will do. As they pass, Skylights lurches clumsily against him, ruffling his lace collar; the hook shoots forth, there is a tearing sound and one screech, then the body is kicked aside, and the pirates pass on. He has not even taken the cigars from his mouth.
I think that is enough to establish that Hook is evil and a villain in the book Peter Pan.
Of course there are many movie, television, comic book, etc., versions of Peter Pan, and in some of them Hook doesn't act as evil as in other versions.
But in any version where Hook is identified as a pirate, he is by definition evil, and so is a villain in the story, even versions where he is not the only villain and where his opponents are also villains.