It means I wont contribute, I wont take part. "We're going to rob the train, do you want to join us?" No, I'll have no hand in it.

This means you'll have no part in something. Usually said when someone wants you to do something bad. You'd say "I'll have no hand in it!"

No. To me it means that I'll not participate in something that is happening. ex: I'll have no hand in the robbery. I will not participate in the robbery.