It's hard being put on the spot in front of a group of people especially if you're not close with them. I'm the same way where I instantly think of my stutter before I speak and my neck just tenses up. On Tuesday, I had to go to the bank to dispute a fraud charge and then I had to take my car to the dealership for an oil change. Both of these situations were rough for me but I eventually got through it. I just chalk it up as a bad day because we all have bad days. That's a tough situation. You don't want to speak in front of a group of people but you also don't want to make a bad impression on the undergrads. I'd probably laugh and then spit out something like, "I love it here but I can't talk in front of people" and smile afterwards. Obviously people would understand after hearing the stutter. I know some stutterers would prefer to not "give up" but there's just some situations where we are too uncomfortable to deal with it. It's perfectly fine to pick your own battles.