In France it is very exceptional to have a woman doctor as urologist, all are men doctors in my experience.
Normally they don't ask to a patient to be naked, only to remove his clothes including underwear below the waist.
Anyway, as regards the question pulldown underwear or take them off, it seems to me according to my experiences since childhood that it was rather taking them off while I was still young under 18 or even 21 age, I was always told to undress at least in briefs at school physical examinations and sometimes naked , when I was in brief, it was the woman doctor who asked me to take it off rather then to pull it down or the nurse until high school, it was not an issue at high school because I was already stark naked when I entered in the room examination.
When I went by myself to see a doctor being under 18 aged, it was the doctor who pulled down my brief when necessary rather than taking them off .
After at mandatory job examinations, when I was still a young man, it was depending on the doctors, either I was naked after undressing in a small locker room adjacent to the examination room , either I was in brief and generally I was asked to pull it down or more often to remove it with women doctors especially for the inspection of the spine and check ogf the gait which was always part of the examination.
But when I went to a private doctor and being older , I have noticed a change, now the doctors are always asking me to pull my brief down, more seldomly to take it off.