I have a moderate stutter and I do training …. Classroom and one-on-one. I love it! One of the things I do is practice the heck out of my presentation. It helps my stutter being confident in the material I am presenting but it also helps me finesse the content. I would suggest practicing at home. Pick any topic and practice. This should hopefully give you the confidence the next time you are asked. Yes, I get made fun of occasionally (one time actually became an HR incident) but that is their problem, not mine.