Eh... my mother was a nurse, so while I can understand not wanting to get into graphic anatomical discussions with one's parents, I may have a skewed perception about how possible those discussions with one's parents actually are, if that makes sense. But yeah, I suggest that using euphemists may at least be the best way to ease them into this sort of discussion, but if they still aren't getting it, then just say what you've said in your original post -- it makes the most sense and even people who aren't nurses would know what it means.
That said, parents are just generally pretty hard to explain this kind of thing to. I never had to "come out" to my parents about this cos 1) my mother has been out of the picture since I was twelve, and she seemed to just brush off all the weird things I did and said as a kid, and the obvious gender identity incongruence was probably just "another one of the weird things the weird kid says" to her. My father died when I was twenty-one, and he obviously picked up on enough to know that I'm "not really a girl", as far as social conventions go, but enough other things to know that I'm "not a lesbian" (and knowing him, he was glad of this).