I'd like to think most probably, Greyworm was talked/convinced/outsmarted/tricked into a negotiation (it could also be absolutely bad writing).
When the scene started off, Greyworm was in no mood to let Jon go.
SANSA: Where's Jon?
GREYWORM: He is our prisoner.
SANSA: So is Lord Tyrion. They were both to be brought to this
GREYWORM: We will decide what we do with our prisoners. This is our
SANSA: If you look outside the walls of your city, you'll find
thousands of Northmen who will explain to you why harming Jon Snow is
not in your interest.
GREYWORM: And you will find thousands of Unsullied who believe that it
The first instance of Greyworm succumbing to the lords and ladies is when Davos starts speaking.
DAVOS: Friends, please. We've been cutting each other's throats long
enough. Torgo Nudho. Am I saying that properly? If it weren't for you
and your men, we would've lost the war with the dead. This country
owes you a debt it can never repay, but let us try. There is land in
the Reach. Good land. The people that used to live there are gone.
Make it your own. Start your own house with the Unsullied as your
bannermen. We've had enough war. Thousands of you, thousands of them.
You know how it ends. We need to find a better way.
GREYWORM: We do not need payment. We need justice. Jon Snow cannot go
From a firm "No, he should be harmed", Greyworm came down to a "Jon Snow cannot go free." - Davos connected to Greyworm in a common man level and not how haughtily the rest of them spoke to Greyworm. He tried to reason with Greyworm at the same time sympathising with the Unsullied.
Next, it was Greyworm vs Tyrion. A soldier who abides by orders vs a guy who can talk himself out of/about any situation. Tyrion can be very smooth when he wants to, and at that moment, the smart Tyrion further convinced Greyworm.
GREYWORM: We do not need payment. We need justice. Jon Snow cannot go free
TYRION: It's not for you to decide.
GREYWORM: You are not here to speak! Everyone has heard enough words
TYRION: You're right. And no one's any better for it. But it's not for
you to decide. Jon committed his crime here. His fate is for our king
to decide. Or our queen.
SANSA: We don't have a king or queen.
TYRION: You're the most powerful people in Westeros. Choose one. Make
your choice, then....
SANSA: Who, then?
TYRION: I've had nothing to do but think these past few weeks. About
our bloody history. About the mistakes we've made......And who
has a better story than Bran the Broken? The boy who fell from a high
tower and lived. ....
SANSA: Bran has no interest in ruling and he can't father children.
TYRION: Good. Sons of kings can be cruel and stupid, as you well know.
His will never torment us. That is the wheel our queen wanted to
break. From now on, rulers will not be born....
Notice that here Greyworm no longer speaks, he is well dominated by the lords and ladies. By now, the situation has passed almost out of his hand. And with "that is the wheel our queen wanted to break", Tyrion did a mic drop aimed solely at Greyworm.
Finally, Tyrion tells Jon
TYRION: The Unsullied wanted your head of course, but Grey Worm has
accepted the justice of a life sentence.
At the end of the day, Greyworm isnt a king, he is no ruler, he has no ruler and he does't really know administration, negotiations or the ways of how the people in the highest position carry out things, especially in Westeros. He took what he got and left.
Finally to conclude,
Grey Worm couldn't kill Jon Snow as he wasn't in a position to do so (or bad writing). He was talked into "king must decide and that the king would be chosen by lords and ladies" as it was reasonable. Greyworm was no king as Tyrion pointed, nor did Greyworm know if/that he could act like one.
And no he wasn't afraid of battle or war. He just got talked into choosing a king and banishing Jon.