I have been a professor for the last 14 years and before that I was a TA/RA for three years while completing my PhD. I also stuttered terribly for the first 20 some years of my life. It was very difficult transitioning from someone who couldn't say their name fluently to someone teaching 200 students at a time. All I can say is that mastery of your material is a major influence on speaking fluently. In subjects I know well, which is mainly developmental psychology, I stutter very infrequently; in subjects I am either learning or have less mastery of, my stutter creeps back up. Good luck.