I’ve been a barista for 2 years as a part time job while I’m at uni. Although l only have a mild stutter, l honestly don’t think it matters that much as long as you’re confident and friendly. I think my coworkers and boss honestly didn’t notice until half a year in because l chose my words carefully and was pretty quiet and worked hard. I kind of have a script down pact to push through any blocks. Just learn what works and use those phrases and you’ll find you’ll get a roll on. You’ll be fine!!!