Just retired as a cop. I have never let my stutter stop me at least trying what I want to do. Never fear the interactions with people. One of the best skills as a cop is a listener. Far too many cops like the sound of their own voice in an interview/interaction. Let your suspect/victim do the talking, prompt them as necessary. if you're going to block, find a way to rephrase the question, use that time wisely, make it a better question. You may not need to ask it. Hopefully your partner doesn't fill the silence. I had some feedback after giving evidence in court. Once I had been asked a question took my time to answer, not minutes obviously, but the feedback was they like that I took the time to answer the questions clearly and concisely. My evidence was usually of a technical nature so I had to make it simples for a judge and jury to understand, so to be honest my stutter worked to my benefit. If I blocked, I apologised to the Judge and rephrased. Never had an issue. Have i had the piss ripped out of me by colleagues, sure, but they know they'll get it back on the same scale, never about my stutter though. Know your stuff and be good at the job. people respect that, villians maybe less so.