In most health institutions, you can have a chaperone of the desired sex to make sure nobody does anything illicit with you. But no, you can't specify that all people who work with you are one gender or the other. And no, your chaperone is not guaranteed to have any medical training (although in practice, they will be somebody from the office).
You can try, but you'll get laughed at. No, you're not going to clear women from the room.
Admittedly, when talking about rape, it isn't uncommon to women to ask for all female staff, and the institution MIGHT try to be accommodating, but it's nothing I'd count on. Frankly, I don't know what happens when guys talk about being raped. My guess is that they would try to be accommodating, but because most medical institutions are mostly female, that could be very difficult.
If this is a matter of modesty, I assure you - they've seen it all before. And then some.