Stutters cause all kinds of insecurity and self doubt. Honestly, if you find a girl that likes you for you, she won't care. I've had a lot of girlfriends in my time and they really dont mind at all. It's the same with everyone, if they actually want to hear what you have to say, they will wait and are happy to do it. You are not a burden on them. If you think that you are then it's only what you think, not them.