FWIW, I had bad knee pain at one point (I shifted to barefoot shoes partly because it helped fix it); when it was at a level where it hurt to walk from the Tube station to the climbing wall, it didn't hurt at all to climb.

And that was bouldering, where your knees do soak up a bit of impact when you land. Top-roping can be pretty much impact-free.

There are occasional movement techniques (e.g. drop knees/Egyptians) which can put torque through the knee joint, but they're not so indispensible you can't easily avoid them if needed.

You'd be welcome to ask in disobey_gravity, btw; I'm fairly sure there'd be people there who can provide more advice.

Also: CLIMBING IS THE BEST EVER YOU SHOULD TOTALLY GO FOR IT. *g*