I know he has the best voice therapists in the world and there's no chance he'll ever read this but: kazoo. That's my advice for anyone who has to give a speech or get their voice in shape for any reason. Ukulele & a kazoo 45 minutes every day.
As a professional singer and former researcher at the National Institute for Voice and Speech, I call bullshit here. Being "pushed" out of your normal range will not automatically cause the same kinds of improvements as weight-lifting does for skeletal muscles. It's just not that simple. It's especially not that simple if you have a paralyzed vocal fold.
That makes perfect sense for breath training, I came upon the kazoo after reading that an early 1900s opera singer never did vocal exercises, she just hummed to warm up. The kazoo works the breath and the vocal cords which are tougher than other muscles, so you can and should work them everyday without fear of injury.
Humming is a vocal exercise. It engages the vocal cords.
Not sure why you think humming/playing kazoo should be a good exercise for someone who has damage in the vocal cords. E.g. the common medical advice for someone who with a hoarse throat (due to a cold etc) is to let it rest, i.e., refrain from speaking. But I'd be happy to see studies proving that wrong.
The vocal folds are emphatically NOT tougher than other muscles. They are in fact quite fragile and easy to damage compared to other muscles. It is irresponsible of you to post this.
I think the idea was not "breath training" but to reinforce the muscles in the walls of the throat which can relax and obstruct the airway causing apnea.