Yes I'd push here too. I don't really care about the tightness of the shorty because unknown shortys suck. And with his stats, the full stack guy you're really concerned about will raise with AA at the very least. Even if he doesn't reraise with anything preflop, AA is still the only hand you're a huge dog to. You're so often good against his range here and you want this short guys stack to yourself.

But it's especially right in your initial situation, because if this guy's a donkey then there's a chance he could call with AQ or even AJ. Donkeys seem to get excited in reraised pots and decide to call.