That is a toss up.
I only kill things that I eat, because otherwise I feel as though I have killed in vain.
Eating the animal is a form of respect and so I do not feel as though the life was wasted.
If I saw that squirrel I would shoot it. I would then force myself to eat the animal, as much as I dislike eating squirrels.
Finally, I would make a really neat mount for the man cave. Probably put him in that same pose or one similar on a branch and hang it artistically from the wall.
You would be showing the animal respect each time you shared your story with someone that was visiting.