Its definately cognitive. Fake your confidence till you make it, by forgetting you stutter. Stuttering is no more than a tunnelvision, and to get out you focus on the external world while speaking. You dont need to be convinced that you can talk fluently, you are born talking fluently and you are only scared. Prove yourself you dont have to be OP i believe you, also if you know it has this much impact on you be upfront about it with your work and find a job with working hours that fit you!