I'm an experienced guitar player who has had issues with my hands/arms (actually unrelated to guitar)... Because of this I am very carefully about not playing in any ways that could cause injury.

I play a lot of Hendrix and am wondering if there are any guitarists out there who play Hendrix songs without using their thumb to play the bass notes? And if so, how? I normally play with my thumb over the fretboard because of the size of my hands but at the same time using my thumb to play the bass notes puts my hand/wrist in an odd position (and probably does for most people who don't have hands and fingers like Hendrix had).
There are some things you can't play that way. You are right that the thumb wrap can stress hands a lot more, I find the index finger especially, since there is a twist thing going on there. Hendrix did a lot of barre stuff as well, but some stuff just needs the thumb wrap, and there's no way around it.

But just try your own thing for the stuff you can't quite do. That's part of what makes every guitarist unique, all our little quirks, hand sizes, who we learned from, and all that.