It will not matter with patients because they tend to prefer more casual relationships with their healthcare providers now a days. If your patients perception is that you understand, respect, and care for them then a stutter will not matter.
However, I think that stuttering will is a challenge you will have to manage or overcome to be a surgeon. From what I have seen surgeons do care about presentation ability and timeliness when responding to questions. For example, when you're in an OR the surgeons may ask you questions that will require you to explain things to them to demonstrate that you have adequate understanding. Also, you must be able to clearly and quickly communicate with colleagues in the OR. Stuttering may be misinterpreted as not responding well to questions or not communicating well. These situations may also be stressful which tends to cause people to stutter more.
You have four years to get a handle on it, though. If I were you I would read about how to reduce or limit stuttering and possibly seek treatment with a speech language pathologist. I had a friend who was able to eliminate their stutter with treatment.