This is more from the American/British perspective as I think had the Soviet’s got their hands on a living Hitler, the answer would be very different.
I find it a fascinating thought experiment to consider how Hitlers capture, trial (would he have been with the rest at Nuremburg?) and almost certainly execution would have played out, but I’m curious if there was an actual plan in place for his capture and how it’s aftermath would have been handled?
More can always be said, but this older answer might be of interest for you.