That’s why you don’t have to explicitly add it as a qualifier at every instance in which it’s implied in your work of non fiction for a general audience.

I think if you aren't deeply concerned with the axiom of choice in your work about infinity for a general audience, then the entire affair is rather farcical. Most of the "weird" stuff about infinity derives from the axiom, after all. A book about infinity, for the lay person in particular, must be in large part a book about the axiom of choice.