I have a mate who stuttered a lot and we were both up for the chop in front of the principal nearly 50 years ago..a mid air collision solved his problems. Word perfect mayday and a safe landing in a small field proved he was up to the job. Retired a couple of years ago from a legacy carrier.
Now I dont suggest that you try that.
I stutter sometimes especially when tired and stressed but I have zero problems in aviation and still do some extremely risky exacting flying. Perhaps NLP might help on a personal note.
In my case it was dealing with bully boys in authority (started with a paedo english master at school).