I took the Goethe B1 exam a couple of years ago and I was also very nervous for the oral part. We were two students during the oral exam and we had to carry a conversation with each other. Fortunately or unfortunately the other person was way below B1 level and couldn't even carry the conversation so my stuttering wasn't the main attraction. I guess what I want to say is: you may stutter and feel insecure during the exam but if you know your German you should be able to pass the exam without any problem