Climbing often definitely helps. Also pull-ups. If you can, you could install a hang-bar in a doorway in your home; some of them don't even need to be screwed into the frame. And you could do pull-ups on those.

But to be fair, I've climbed for twenty-something years without ever having a lot of upper-body strength. My hands and forearms get stronger if I'm climbing a lot, but mostly I just finesse stuff. Technique over strength.