After years training to be a doctor and even working as a home carer, nakedness isn't a big deal. It's basically just part of your job and so the doctor will, in most cases, not care one jot and focus on making sure you don't feel overly uncomfortable! Nakedness as a part of your job does NOT turn you on! For some reason, that helps me at least.
This is your endo. When compared to many of the health professions this is someone that, for the most part, tends to be way less judgemental. It's someone you don't have to explain anything to and would therefore make the procedure less of a tedious task. With other health care professionals you'd be the dude getting a pap smear and it just adds to the awkwardness.
When I was a home carer there were precious few guys in the job and so male clients just had to deal with women having to help them shower or wash. They would feel really uncomfortable about the idea of a woman looking at their downstairs junk and washing them, but they knew they had no choice and after a few sessions they'd realise that we didn't make a big deal of it so they could almost ignore it being uncomfortable. I mean it's difficult enough for anyone to need that kind of help but to not have a choice in gender, that's got to suck a little for sure. Some women were uncomfortable with me because they thought I was a guy but they get over that fast.
For me, I HATE being top or bottom half naked. It's something I don't like. At the same time I know that in order to get top surgery, or even particular exams, or surgeries I've been through, I can't wear anything on my top half and that's horrible but it's for the greater good so I man up. For pap smears - I man up! The fact that you seem to have never had one is a concern in itself, maybe they've seen that from your notes?
The end of the day, if you don't get check ups, you could die. You might be willing to take that risk but the general idea out there is that T may put you at increased rate of downstairs issues. So it's a definite possibility that if you refuse the exam they could stop your scripts. Personally, if you were my patient and you refused this exam and by default a hysto itself (you NEED to have that part examined for a hysto) I'd stop giving you scripts because that's my ass on the line. I can't speak for your endo but it could very well be a possibility. So right now, I'd be looking at ways to overcome your fear and deal with it. EVERYONE has to go through uncomfortable exams they don't want to. Mammography is apparently hell. Pap smears and prostate exams - no one wants them. Yes, we have the added dysphoria about it which makes it worse, but at the end of the day, it's a necessary evil and should be done.