If you watched "Shakespeare in Love," there was a scene when a tailor, Wabash, was preparing for his role in "Romeo and Juliet". He was a stutterer (severe) when he was reading the script. When Willy heard him, he was terrified and was very worried. The actor's friend came him down, telling Willy that once the actor is on the scene, he will be perfectly fluent. Yes, it is possible. When I was a lector in different EE disciplines, I didn't stutter (well, mostly). In my casual life, it happens quite often. The trick: you should imagine yourself as a character who is fluent. That's it!