We will often read aloud to each other in the evenings, and sure enough, he does sit up better! He also has one night a week of voice acting, and I’ve seen him gesticulating to go along with that.I'm not saying that any of those will provide the benefits of, say, regular swimming -- but hopefully you can incorporate both, you know? A little more regular activity through goofing around, and some more planned, intense, activities.
One additional thought: since he used to be in theatre, possibly instead of home karaoke instead do some play readings together? Still going to demand breath control and maybe gets him to sit up a bit straighter and so forth? (so long as he wouldn't see that as pandering or something)
Also, being in my early 50s, I can attest that even at under half his size it certainly can be hard to get my butt up off the computer chair and out for a walk. Transitions just seem to be more effort than they used to be, and the instant energy to 'just do it' is not there anymore. Best of luck on helping him deal with the twin challenges of general aging and his size.
He also takes great joy in playing with our 2 cats with their “fun sticks,” and his “arm stamina” has improved with this. He also will bounce his cane around for them, which they find FASCINATING.
So, with those activities as a foundation, more fun around-the-house things will be doable and enjoyable.