Definitely practice what you're going to say. Like you, I'm fine if I can substitute words; it's when a word is non-negotiable that I suffer. Practicing helps, though stuttering being what it is, it's unlikely to be a cure-all. But a lot of your stress is coming from the fear of being found out (which ironically then adds to the likelihood that you might stutter). So it would make sense to get rid of that fear. Why not just say to your supervisor, "Just so you know, I have a mild stutter, so if I stumble a little on my words, that's what's going on." Sound chill about it and she'll be chill, too. And I bet you'll then find that the stress factor goes down considerably, helping you be more fluent.