I have a very similar role in that I lead project teams, and present frequently for the executive team. Really, the only way to erase the doubt is to kill it in the next interview. If they were hiring a software engineer, and required the person to submit code, the person would only get so far by saying they don’t code well in high pressure situations. Sadly, the only way is to actually perform well. I find interviews are much easier once you remove the intimidation factor. You’re smart. The hiring manager likes you. Remove the pressure of it being a job interview, and look at it like you’re talking to your friend about this job you want. Also, I don’t believe stuttering is recognized as a disability, so even if they didn’t hire you solely because of your stutter, there isn’t much legal recourse.