Sorry to hear of your injury. Rope jumping can be a good endurance exercise especially if you can maintain it for 40 minutes at a time. That’s actually quite impressive in fact because most people will struggle to jump rope for more than a just a few minutes. It may be that moving to so much long duration rope jumping like you propose will have its own injury potential unless you are very well conditioned for it. Other options while you are healing this knee injury are walking on an inclined treadmill or stair machine and cycling. A mix of all these things may be the best approach. I am just concerned that 40 minutes of jumping rope every day will soon cause a problem for your Achilles tendons or calf muscles.