Help! 2nd pair versus villain with 40BB

[runway model]

NL$200, Hero opens to $8 in the CO with A9s, and the Button, who has TAG-ish stats and a stack of just over 40BB, calls. The blinds fold.

Flop is K93 rainbow.

What's the plan?

1) I don't want commit 40BB on second pair
2) But any bet or call on the flop is going to put 1/3 or so of eff stacks in.
3) I don't want to fold yet
4) If villain has hands like QJ, QT or JT, then these have 10 outs. So i'd prefer to avoid giving free cards

What's best. C-bet flop then give up? c/c flop then give up? c/f flop?