I think your fear could be dealt with like social anxiety. While the anxiety you feel is very real, strangers being “interrupted” by you and eavesdropping on you likely isn’t real. Out and about, people are in their own worlds. Everyone is too preoccupied with their day to notice you stuttering, especially if you are talking to somebody else. Unless you are unusually loud you aren’t interrupting anyone. More importantly, so what if you did? Would it really be so bad to simply be noticed by a stranger? Anything can make someone lose their focus. They’d forget the interruption almost instantly because overhearing a stutter is not memorable.