I don't have kids, but my mother has told me multiple times how she went through exactly what you're going through. Living with a stutter is tough, but if it truly is a stutter, it's not like taking them to a speech pathologist is going to fix it. It isn't something to be 'cured' it's something to be managed. And you being a parent who grew up with a stutter is arguably one of the best resources a kid with a stutter can have. Someone who gives a judgement free zone, someone to teach them the tricks that we all develop to manage our stutters and most importantly, someone who understands them. Just let it be man, your child already has the most valuable asset someone with a stutter can have; a parent to show them that your stutter can be managed and doesn't define who you are.