In this scenario Player #1 has the Trade Hands and Stop That, and Player #2 is being forced to trade hands.
A: No. If the surprise were in Player #2’s hand, then Player#2 could use it to stop the Action, but if the surprise is in Player #1’s hand, then Player #2 does not have access to the card until after the Trade Hands Action has been resolved, by which time it’s too late to be stopped.
If you think about it too hard, you’ll realize it can ONLY work this way. If it worked the way you described there would be a paradoxical loop:
You used the Stop That you received in Trade Hands to stop Trade Hands, so you didn’t trade hands, so you didn’t have the Stop That, so you couldn’t use it, so you traded hands, but then you had the Stop That, and you used it to prevent the Trade Hands, but then you didn’t have it, didn’t use it, but then you traded and had it…
…and so forth to insanity.