At first I liked ShoveorFolds ironic call suggestion, because I thought the equity difference on a non AK high board against KK+/AKo/AKs would be bigger than it is. Against that range you're 40% pre, and roughly 45/55 on a none A/K board.
If you ever think he does this with AQ or JJ, or as a bluff... EVER, then shove. If not
fold. I think that against most players at 10nl in this situation, it's just a high variance shove that you can choose to take... a lot of people will 4bet JJ+, especially if you've 3bet him prevously.