A piece of paper is all you'd have to prove a spay though.
Not to mention, while there probably are some vets that would do it for the right price, that's a LOT of hassel to go through
just so you can compete in AKC events.
You can't get a CH, you can't register litters.... ALL you can do is compete in their flyball, agility, rally, etc...
I'm not really sure anyone would go through THAT much trouble(and risk their license as a vet) for such a meaningless thing.
I can compete in other venues without issue, AKC just happens to have more events local to me...