um the ENTIRE problem with this hand is that you sat down with 40bbs. don't do that and this hand becomes 100000 times easier.
If you are trying to play shortstacked, but your stack is such that you aren't happy about getting it all in after the flop with AA then you really need to adjust your buy in size. Raise more preflop and c-bet more as well, because your goal here should be to commit yourself as quickly as possible.
If you buy in w/ $6-7, raise $1 pf and c-bet 1.75 on the flop, then this hand is obviously a no brainer.
Anyways you can't fold this this short, and i don't really see why the Kc is such a scare card since villain's peeling range involves alot more than a K (not to mention the very fact the K came on the turn reduces the odds
of villain having it). I'd probably bet call shove here on turn unless villain is really aggressive and likely to try and shove turn as a bluff, in which case if you c/c you'll have gain a little more value from the occasional bluff. Still i like bet-call shove, as villain could check behind with many hands that aren't going to call certain rivers (pps w/a diamond etc).
In nl25, when faced with a short stack I certainly think ppl get involved in pots that they shouldn't, because they figure it can't cost them all that much money, so you could get called here with some pretty random hands i think. Fact remains, however, that you simply cannot play shortstacked and ever fold AA.