There's nothing wrong shutting down with a whiffed AK at 2NL, especially when the whole table sees the flop with you.

I don't mind how you played the hand but I prefer a 1/2 pot bet for value on that river. If somebody raises you then re-evaluate but it really doesn't look like anybody has a Q or a 9 at this point.

It is very likely that somebody else has an Ace because people at 2NL love to call with Ax.

What was your plan on the river if button bet 1/2 pot after you checked? If your answer is call, then you should probably bet because people will generally call with a much wider range than they will bet with. It's quite possible to get value out of K or J high here too imo.