You can do it, I'm 49. Find the way you like to climb rope and just do it a lot. Buy a 1000 ct. bottle of ibuprofen. There is no exercise for climbing but climbing. It hurts for a while but if you climb consistently you'll get past it.
I also can see 50 on the horizon, and a good daily stretching regimen goes a long way to lessen pain at the end of the day. Get those muscles warmed up before you put them to work.
pantin and hand ascender will help a lot. It will allow you to focus on your climb and not on how fatigued you are.
The hand ascender (I'd suggest a double handled ascended) will allow you to work on your arm strength while keeping your hands a bit protected. It will also help because you won't have to grip a 11mm rope but instead a nice, contoured handle.
Climbing is the best way to get fit for climbing but not the only way. I'd suggest working on your core muscles and arms. Your abs are gonna scream with your first footlock and long body thrust. Your arms are gonna do the same. Legs are important as well for footlocking but there are other ascent methods you can use to avoid the rigourous workout that footlocking provides (mainly srt but it can get a little pricey with certain systems)