They don't even need to know about birth control.
Oh, I beg to differ with that opinion. If a woman is a nymphomaniac - that means she's almost constantly wanting sex. And if she happens to have sex serially with someone who believes that it's in fact, her responsibility to see to her own health and safety, (which is most men, by the way) that could result in a whole lot of kids.
But I guess if you're a nymphomaniac too - you guys can be nymphomaniacs together and then, as you said, you'd make the birth control your responsibility.
Sounds like a busy, but okay plan.