Help with my 10yr old son’s worsening stutter

Help with my 10yr old son’s worsening stutter My son has stuttered since he was around 3-4 years old. It’s a part of who he is. Nobody really acknowledges it bc we don’t want him to feel bad about it. As his mom I notice the little changes in what sounds are harder than others at a given time. Throughout the years it will change, like sometimes it will be a S sound sometimes it will be D sound sometimes it will be the 1st word of a sentence and just overall the way he stutters will change every now and then. He went to speech for a little bit in first grade and basically I was told that he’s very smart if it goes away goes away if not he’ll just have to adjust. I have suggested speech therapy outside of the school to his dad (who controls all his insurance) and he is extremely against it. I think his dad sees getting my son help as a bad thing, like there’s something wrong with him if we do that. Anyways he’s now in fourth grade. He has a great social life and I noticed just very recently that he is stuttering much worse. It’s taking him a lot longer just to say one word and it will be multiple words throughout each sentence that he struggles with. It is taking him a long time to get through one sentence. I’m so worried about him. I also feel like he’s just becoming more self-aware and maybe he starting to look out for cues on other people which is causing him to feel more self-conscious when he’s stuttering. So today I decided to talk to him about it. He says when it happens he feels like he can’t breathe. And I have noticed when he’s trying to get a word out he’s almost like holding his breath or trying to take a deep breath and his neck kind of tenses up and his eyes get big. So I suggested maybe just trying to slow down (this is really the only thing we’ve ever said to him when he’s having a hard time) and focus on regulating your breathing when that happens.. But I just feel like I don’t know how to help him even though I want to so much. How can I help my baby without making him self conscious or even making him focus on it more than he needs to. I feel like focusing on it could make it worse? Help