(1) He didn't 3bet.. You did. He 4bet you.
(2) Your 3bet preflop is obviously correct, and if he only 4bets with KK+, AK, with the dead money in the pot and your 47% equity, you are obviously +EV to shove it in.
(3) This is blind v blind, so you should likely have a bit wider of a 3betting range, and if he realizes this then he should be stacking off lighter, and 4bet bluffing with some frequency. Meaning he is likely surely 4bet/calling QQ+, AK, and might bluff some hands.

So getting KK in here is definately +EV, and correct. On top of that, your logic for wanting to flat and see if an Ace drops is wrong. Say he will stack off preflop with QQ+, AK, then you have 57% equity, and he is stacking off with 21 combos. However, postflop if an A/K doesn't drop he might still stack off with QQ+, but is likely not doing anything other than cbetting AK (if he even cbets AK whiffed in a 4bet pot). And on the flop now you only have 50% equity against a stackoff range of QQ+ (on undercard flops).

So get the money in preflop here if you feel his 4betting range is strictly value. Now if you knew he was 4b bluffing with a large frequency, then you could think about flatting his 4bet and playing poker postflop, as you expect him to fold a very large % of his range to a shove. In which, you are likely going to be ahead of most of that range on most flops. But that's likely not the case, so just shove it in preflop.