I use a phone a lot and some times in high pressure situations on faults. I'm a signal electrician for a city rail network. One thing I found that helps me for all conversations with people I don't know is a very well practiced happy upbeat greeting I know I can say confidently. For me it's just "hi how are you?" in a really happy voice. From my experience and catches people of guard a little and brightens their day a little. It puts you in a positive light for them straight away so even if you stutter after that they are much more patient and understanding. The more you do it. The less anxious you'll be and the less you'll stutter. As long as you are doing your job competently people won't care. The train controllers at my work probably know me as the guy who stutters but they also know if they get the guy who stutters, shit will get fixed.