I've been on both sides of this as someone with a stutter and a service industry worker. If you don't want to stutter in front of a big group like that, wait and watch where they go to put in their order. Sometimes the server is just standing alone at alittle station. You can do what you did and just walk up and maybe explain your situation and try to order what you want. Ultimately, the servers are there to accommodate everyone and make a good tip and won't mind. Hope this helps.