Good on you for not lapsing into the easy way out and trying to work on the weak spots. Though climbing seems like serious enough exercise to me :D
As you said, I think the important thing is finding one that works for you, because if you're gonna force yourself to do it just for the health benefits, it won't work.
Especially if it's as a preventative. Often we won't do anything about our health until we reach a point where it's impacting us directly. Many won't even do anything then either.
I have to consciously not avoid the styles that require more leg work and short burst energy. 😅