I think you’re overthinking it a little too much tbh . I’ve stuttered my way through plenty of job interviews where customer interaction was part of the job duties , including a job as a tutor where I essentially did all the talking . My stutter never presented an issue to the interviewers and I would categorize mine as moderate where it is definitely noticeable in just about every sentence . This is really more about making you more comfortable stuttering during your interview. Just a quick sentence to let them know what’s up should do.