I'm not a docter but I work in mental health care. Talking to patients is a big part of my job. What I found out during my job is that, the more comfortable I got in my job, the less the stuttering i had. That maybe different for you, but my patients really listen to me and they don't mind the stuttering at all. For me, body language and feeling comfortable in my job is important. That is something you have to grow and go through. I believe if you go through with the hardship, you'll become a good docter and people don't mind the stutter. They just want you to fix them.