I would seek out an slp over a communication coach. They wouldn't know anything about stuttering, it's a very complex condition. Also a good slp should also know how to help improve communication. As far as finding a good slp, that can be a challenge as many don't really know how to help. You can try reaching out to the national stuttering association or stuttering foundation to see if they can recommend any SLPs near you. Also if there's a university in your state that has a good speech and hearing department, particularly one that does stuttering research, you could reach out to them to see if they could recommend anyone near you.