I did my GCSEs 5 or so years ago and I was in a similar situation to you. If you are doing another language, I did GCSE French, you can get a doctor's note acknowledging your stutter and it will allow you more time in your exam and maybe the ability to pause. This really helped me out a lot and if you have any other speaking exams this is definitely worth looking into if you have any other speaking exams. It's also good asking if you can practice going over it first with one person in the room, then 2, then 3 and so in. This is what I did for my English and just getting used to being aware of other people while you do your exam