I don't think I like it, and here's why. Anything that calls your all-in likely has you beat, and will reduce your outs. Those hands are likely to be AA, KK, or any other set. If he has any of those hands, your A outs are no longer good. Your K outs will also be dead unless vilain has AA. Thus, if villain calls, you only have a flush draw and MAYBE 2 more outs.

If villain doesn't have one of those hands, he will likely fold. In which case, your AK would have been good anyways, and you could have gotten more value.

The fact that villain min-raise and then bet relatively small worries me.