I do not see what everyone interprets as the infinite loop starts within the wormhole. I see the point of origin for the infinite loop within the black hole.
While he does see himself in the wormhole and shakes Amelia's hand, the wormhole was a place along said timeline. Where I contradict myself is we cannot tell if it is an infinite loop because we only view this movie timeline as linear. We do not have knowledge that Cooper went back in time and repetitively enacts the same action(s) over and over again. We only see him do it in two occasions, but his travel back through the wormhole for a handshake, shows us that Cooper can see his past-self in the ship.
Inside the black hole, somewhere near or at the singularity, Copper realizes that "they" are not bound by time and space, but realizes he belongs to "they." Even though the tesseract closes, it was not until after the tesseract was closed that Cooper became capable of crossing time and space.
So, my thesis is Cooper did not have an infinite loop because he went through a wormhole, but because he used Newton's third law to experience the black hole and time-traveled from there. The handshake was a stop before continuing forward, while showing us the ability to travel into the past, then the future by Saturn.
Also, he is able to travel to the past when he isolates a point in time in Murphy's room but may be right when he stops and maybe hits the singularity.
Seeing the distortion for the first time and Amelia shake the hand of the being, while also realizing in the near future that he is the one that distorted it, let's me believe that it is a loop, even after having the ability to move forward on his timeline because when wormhole Cooper sees the distortion and distorted Cooper acknowledges his presence there at that time, then allowing wormhole Cooper to do the same when he becomes distorted Cooper.
Theoretically, is it possible to travel to the past without changing anything and creating an infinite loop? As fifth dimensional beings, they went back in time and began changing gravity, creating wormholes, and guiding the three dimensional beings. I feel that one cannot go back in time without creating an infinite loop. Going forward could work but then, if we are allowed to visually manifest our future, we would be given the choice to remain on our set-path or choose to betray our "destiny."
To not create an infinite loop with the past, I feel we must be exactly what was explained when going through the wormhole: "Instruments won't work here. All we can do is observe and record." If it weren't an infinite loop, wormhole Cooper should not have been able to see the invisible and distorted Cooper. Then again, like Donnie Darko, he could have been a finite loop because he was required to do something that required change and until he did, was an infinite loop.