My school is a lot smaller than yours (3k) but my experience with the ice breakers we did is that you don’t have to overdo it if you aren’t comfortable talking at first. I never felt like I was in a situation where I was forced to talk besides the very beginning when you introduce yourself. I was one of the more talkative people in the group and stuttered a few times and no one (including me) ever acknowledged it. We were in groups of roughly 10 students and two leaders.