I'd advise against doing this. They're interviewing you, not a prerecording of you. They'd almost certainly be able to tell it's a recording and it's not actually you. Even if you tell them you're using recordings for your answers, it comes off as unauthentic. Explain you stutter. Explain when you're nervous it gets worse. Also explain that even though you stutter, it doesn't effect your work (that one is important).