Your intentions are in the right place, and I'm sure he will appreciate that. I know it's easy for a stutterer to "shut off" when the topic of stuttering and moreso improving the stutter comes up. I might suggest framing it in the way that first and foremost, you love him! You love him and only want the best for him, even if he stutters every word he speaks. If you frame it in a way that tells him you want him to improve himself for HIMSELF, not for you. To improve his stutter not because of the stutter itself, but because it makes him a happier, more complete person. Exercise (both vocal and physical) has a definite effect on fluency, so that certainly can be worked on. It's a little different from social anxiety in that it compounds. It's a stutter, AND the anxiety from having a stutter, AND the depression of having a stutter, AND the feelings of incompleteness or inferiority from having a stutter. A lot of people give up because they don't see improvements, no matter how much it may bother them. It's not easy, but support and love make all the difference, both of which he seems to have. Cheers!