You could try coming up with the word order of the first sentence you're going to speak when you up and chat someone up. That might give you the confidence to overcome this initial block. Mild stutterers like you and me can certainly be lacking confidence when we start talking to people, if we get very concerned about our problem. Also, it wouldn't hurt to record your voice secretly with a cell phone app, while you're talking to people. Observing our own speech can really be eye opening, when it comes to finding larger patterns where we need to fix the way we approach our conversations. I think of it as kind of like looking in the mirror before I leave the house in the morning. Finally, make sure you have a good, even flow of breath coming up through your larynx before you start talking. This is something they teach you when you're a chorister in a choir.