That is assuming the Soviets would have handed him over. I bet Stalin would have him flown to Moscow for the biggest show trial ever. Ignoring most of his other henious crimes to focus on what he did to the Slavic people of the Soviet Union.
Followed by a bullet the head unless Stalin would have asked for some special public execution but I doubt it.
If Hitler had been captured he'd almost certainly have been captured by the Soviets and the chances he'd make it to Nuremberg are quite slim. He may have been publicly executed or just disappeared. Considering how many soviet lives were lost in WW2 it'd be unsurprising if the officer in charge of his capture didn't just take matters into their own hands over a personal grudge.
It's not though. The question makes the assumption that he would have been handed over for the Nuremberg trials.
But the Soviets were fucking ruthless against Nazi Germany. They were REALLY driven by hatred for them. If a Nazi soldier surrendered to Russians, a summary bullet to the head was often the more merciful outcome.
And it was the Russians that would have found Hitler first, so it's far more likely that they would:
execute him on-the-spot
torture him until death
have their own trial for him in Russia before torture/execution.
What was it called when they would strap you to a raft, cover you with milk and honey while also force feeding you milk and honey so that you're slowly eaten by bugs and birds and stuff while also shitting yourself to death?