I'm sorry to hear that but by skipping the icebreaker you are just enabling your fear and not really going to get better by avoiding the situation. I would stutter during the icebreakers, and during most public speaking scenarios, but I'd rather stutter than avoid it. To me it's more awkward to be the only one avoiding the situation than to stutter. But everyone is different and has different experiences. Only you know why you chose to avoid the situation. Personally, I've never been made fun of so maybe that's why I've been more willing to stutter and not really care what people think. I stutter and I can't always control that so I couldn't care less what people think about it.