Nobody is going to look down on you for having a speech impediment. I personally make minimal effort to hide mine, at work or elsewhere (granted I do not have to deal with the public at my work). The first time I stutter in front of a coworker, I mention how I have a stutter, and usually laugh it off/make light of it. This let's them know that it's no big deal and that it's going to happen so get used to it. While high/middle School me wouldn't say the same thing, the adults in the working world (at least where I am/have been) are professional, and if you can complete your job/are not a totally toxic person, they likely won't give half a rats ass. And if they talk shit they won't do it to your face, but there is nothing you can do about that. At the end of the day though, they know I do good work, I know I do good work, and that all that really matters in the professional world. Keep on keeping on.