The way I play around my stutter is by adding some words beforehand that certainly feel unnatural but is better than clenching your face for a full minute. Like instead of saying your name or saying "my name is ………… ". You start with something like "Oh. The name is ………… ". Second method is speaking with fake tone/accent. I almost never stutter when I speak in sarcastic voice or fake accent. Obviously in this case the conversation is serious. So just try speaking in a different tone (more forward tone/curious sounding tone), than what you sound like when you talk normally. Makes the talk way easier usually. However, please don't over do it. Specially when you're not pressured to stutter. I almost always add these unnatural words and play with my tone a bit before any sentence I know I'll stutter with, so the words can come off my mouth easier. And hence, I developed this weird and unnatural way of speaking. So just don't over do it when you're not pressured.