If i'm entering upon a conversation that is expected to be high stress (and I anticipate my speech to deteriorate), such as a job interview, I open up the conversation by saying "Before we begin, i'd like to first ask for your patience as i have a tendency to stutter/stammer." or however I feel like saying it. A good friend of mine that's in sales suggested this to me, and I tried it a few times. It makes the conversation with random people easier. It sheds some of the weight (expectations), and it makes those small moments less significant. I even found myself to stammer less and just focus on my breathing more. Other social-psychological benefits in the conversation come with this as well.