Can I ask for another physician besides a woman to do my prostate exam?

Depends. First, you should have no reservations about a female doing your exam. If you are just too timid or bashful for a female to do your exam, see how she feels about it. A frank and open discussion should be had. If a male professional is available, perhaps this is not an issue to ask for. Otherwise, you need to plan ahead to find a place where only males provide this care. Ask and be open.