I've been chosen for jobs partly because of my stutter. I was told by employers that my stutter makes me appear honest and approachable. This set me apart from other candidates who appeared to be cut from the same cookie cutter of attitudes and interview platitudes. I simply explained to my interviewers that I have a stutter in new situations and it softens considerably when I settle in. And this has also helped me get promotions and career progression in a rather competitive and cutthroat business. I would suggest the above strategy for your next interview.