A couple of caveats. My stutter was pretty mild, but complicated by some other speech impediments. I have no idea if this works for other people (a quick google search says that it worked for Emily Blunt) When I was a kid I started doing an impression of the SNL Hans and Frans weight lifting bit. A at a picnic someone commented to my mom that I was much easier to understand when I was in character. Fast forward, and I pretty much do an impersonation of my grandfather's accent 24/7. I occasionally fall out of it and I can't read out loud with it. But, it makes my day to day easier. If I had to guess, I would say that its easier to do something well practiced than just "be natural." If your friends ask about it, just be honest. "I am trying a technique to deal with my stutter." So find an accent that fits you or where you live and try to imitate it.