In the past when my stutter was much more visible, I would tell the interviewer early on that I have a stutter that is worse when I'm nervous such as in interviews, but it doesn't affect my confidence nor my ability to communicate effectively. To lower anxiety, I would rehearse the typical interview questions and beg my HR friends to give me mock interviews. For me, the better I was prepared, the better my speech was. If the interviewer can see your confidence, poise and positive attitude through the stutter than you're set.