I hate making calls too..It is good that you already know some docs who will do it though, will make things easier on you.
I called my current doc from my ex therapist's office actually. I think I basically said something like, "Hi, I would like to make an appt with Dr. such and such." Couple months later, had the appt, had all my stuff together already, started hrt that day!
I actually went the other way too. I told my PCP, she referred me to a doc, this one didn't do it, but she referred me to another doc who does do it.
I'd say call around, maybe make more than 1 lol, that's what I did and glad I did it, just in case something goes wrong. See which one can get you in first, which one you feel most comfortable with, one you like the most.
I'd say it would probably be best to give em an idea as to why you are coming. Also, can find out what things they may require or want you to do in the meantime. Maybe can cheat get everything done early