This kind of time machine would violate a fundamental rule that governs the entire universe - that causes happen before effects, and never the other way around. I believe things can’t make themselves impossible. If they could then there’d be nothing to stop the whole universe from descending into chaos. So I think something will always happen that prevents the paradox. Somehow there must be a reason why our scientist will never find himself in a situation where he could shoot himself. And in this case, I’m sorry to say, the wormhole itself is the problem.