Hi there,
I started hormones via informed consent. I got my prescription at my second appointment. During the first appointment, they filled out all of my medical history, went over HRT, discussed my goals/expectations, etc. The only physical exam I had was a general height/weight/blood pressure check. I never had a pelvic or breast exam for HRT or any of my surgical procedures. You should expect to have blood taken at some point prior to starting. Some doctors don't, but it seems most do.
Honestly though, even if you have to, it's a one time thing. You do it once, then you've got your prescription. Build a relationship with your doctor. Explain to them how uncomfortable you are with exams. That is likely the reason why I haven't had any.
Best of luck to you!