I'm going to demand a seperate exam room
That feels a little bit drastic, but why are you going to require a separate exam room?
I'm going to be undressed alone for an hour on a public floor.
I understand why you would want your own room. You may be more likely to get one if you ask nicely because demanding it could sound rude.
I don't need to be nice. I'm privileged so I'm going to get what I want no matter what.
I feel like you will end up being resented by others if you feel like you are free to demand things that other people do not get and feel superior with others. You will end up being a public pariah and you can end up losing your job and your respect from others with how you're treating people, so I suggest you don't feel superior and tone down your privilege claims.