I get it, You're revealing an intimate detail about yourself. That is typically easier in small group settings. This is compounded by the fact that you'll be in a room with your colleagues. There is a risk to it. You're straddling the line between giving the interviewee pertinent information and not seeming defensive about stuttering. I that in both cases the way in which you respond gives clues to others how to respond. If you regard it as just a random piece of information, that gives them permission to treat it as insubstantial. It's a challenge. But in the end even if the "worst case scenario" you're thinking of comes to pass, very little has changed, right? Your work relationships will not change from one relatively small interaction.