I realize this is bending the rules... a lot... but hear me out.
The fact that hes mute would just be for flavor. If something gives no additional perks, then in my opinion it doesn't really matter if it follows conventional rules. I was developing a mute sorcerer with a raven familiar to speak for him. One of his cantrips allowed him to create a ball of fire, so he used this fire to "speak ignan" as his verbal component. In essence, he wasn't mute. It was just a small flavor thing.