Don’t be nervous! You’ve already made it this far, why stop here? If you already have your master’s, then you probably have already dealt with obnoxious people in the field and wherever else. If you want to do it, absolutely go for it and show non-stutterers that you’re able to contribute to whatever your academic community is and overcome adversity in the process :) Also, you’d make a hell of a role model for other people who are interested in pursuing an advanced degree like that. I’m thinking about pursuing an accelerated masters (MPH) and this fear has always been in the back of my mind too. But, I always think that there’s going to be ignorant people no matter where I go so why not try to get into a better place for myself :)