We need the stack sizes, also what do these players think of you, if you cold call the 3b will they assume your just being dumb with KQs or some crap, or will it look like QQ+ or even KK+
Generally cold calling OOP should not be part of your game, so when you do it, it will arise suspicion, perhaps not at live 2/3 and probably not vs a rock's 3b but you should have some 3b'ing image and a cold 4b bluff should be in your arsenal so a cold 4b here shouldn't snap fold out KK, and nothing worse is really stacking off when you 4b anyway, so I'd just 4b, or depending on stack sizes just 4b/ship, essentially do whatever gives you the widest perceived range possible.
EDIT: lol, either your image is sh%t, or that KK guy is a scared nit, or perhaps someone who has a tell on you

If he's 3b'ing JJ+, but only calling with AA, you should 4b him a ton.
JJ+ AK+ is 3% of hands
AA is 0.5% of hands
Depending on stack sizes I would 4b shove something like A5s here, a hand where u have not so terrible equity in case the other guy decides to call you with KK, or 4b/f to the nits ship.