Get him in speech therapy. My mom did this for me when my stutter was getting out of control. I was 8 years old. Then my dad noticed like you that I didn't stutter when I was singing, so he encouraged me to join the children's church choir. Those moments of fluent singing were sublime for me. Even though I didn't stay with the church, I often think back to those moments with pride and joy. Being able to be fluent in front of a huge crowd. The positive experience of singing led me to picking up the guitar and it's become one of my beloved hobbies and makes me happy. At the end of the day, it's about building up small little victories, little moments of joy and those will bolster self-confidence, self-love and demonstrate that there's more to life than worrying about a stutter. Good luck!