Respond back immediately. Get that interview set up and get to it! Do not let your stutter make your decisions for you!!! You're facing a lifetime of regretting avoiding this interview. They're going to be a thousand moments in your future where you look back and regret not having done this interview. As well as the next interview that you don't take. The crush that you want to approach. The raise that you don't ask for. Avoiding things because of your stutter is a horrible habit to get into. I remember one or two really bad stuttering episodes in my life. I remember so many more avoidances. Shots that I never took. I had plenty of bad stuttering episodes, but for the most part those aren't what's stuck with me. It's the regrets that stick with you.