Jump rope is much better exercise for the amount of time you have to do it. 10 minutes of jump rope is equal to running an 8 minute mile.
that said, you will get jumpers knee if you don’t prepare your legs properly. Each day, before you start, you need to do about 10 minutes of squats, leg raises, and other exercises focusing on your knees. Do that for a couple months and your body will adjust to the stress you’re putting on it by jumping every day.
also, don’t try to be a hero out the gate. Start by doing 200 skips a day, let your body adjust, and slowly work your way up to a higher number (I currently do 1200-1600 per day, depending on the day).