People don't react to your stutter. They react to how you react to your stutter. If you going on with the persona of "yes I stutter but I'm OK with it and I'm good at my job" Most people will be fine with it too. You might have to fake it till you make it at the start. My job involves fixing faults on a rail network and the control centre probably knows me as the guys who stutters but they are always happy I've called so they must know if they get the stutter guy shits gonna get fixed.