I had the exact thing happen to me, and since my knee/legs/riding was out of the question, I decided to pick up weight lifting. That was 9 years ago and I WISH I had started earlier. I have ruined a few rides from hard workouts the night before but such is the price of getting better.
You don't need to be fancy or elaborate. I use simple barbells with removable plates and you can do A LOT of exercises with just that: shoulder/chest bicep flies. Or military press or bench press (you will need a bench too, but they can be had cheap especially if used. Going to a child's playground you can do one of the best exercises known: pull ups. Cost nothing but time. Using barbells and heavier weight you can do shoulder shrugs and back pulls. You can do pushups and situps (no weights needed). Once nice thing about free weights and barbells is that you can do them sitting down (flies, presses) and not have to weight bear. Bench press is non-knee loading. I have a bench press rack (I am doing bench as I write this) but the only advice I can give is: stick with it. You will not see results right away but like most things in life you will only get out of it what you put into it. And this is dedication, effort, time and focus. But the gains for riding are huge. Tough technical sections get easier as the upper body is better able to fight off the being bounced around. And the younger one is, the more gains you will see. I know space and time are limiting factors, but we can all say that. I put in about 1.5hr 3-4 times a week plus riding and it is making the time to do it. The initial outlay of cost to the weights might be some cost, but getting weights used is easy since many get into it and give up.
I am not so much a fan of the "all in one cable resistance systems" as they take up too much space and you can do just as well with free weights.
I hope it goes well for you, and stick with it. I am 44 and in the best shape of my life and only wish I did it earlier in life. To say nothing of the personal pride and confidence which is a natural reward for your hard work which in turn offers positive reinforcement to do more/stick with it.