I took the IELTS academic one. If you feel uncomfortable, you might get a diagnosis of your stutter from a doctor, which can be used in IELTS to extend the exam's time. Also, if they know you stutter, they shouldn't discount any points for the stuttering -- they're only concerned with your English ability. By the way, I felt quite confident of my performance in speaking section, but tumbled completely! A lot of it was was because I wasn't well prepared (I though I was when practicing alone at home), so make sure to practice with somebody to imitate the exam setting. This will help immensely and will reduce stress!