I strongly recommend that you remain as active as you can, even if you're feeling pain or discomfort from your hypermobility symptoms. Your body wants to move, and the stronger your muscles and ligaments are, the less strain your hypermobile joints will be under. I lift weights 4 or 5 times a week, and I undertake short cardio workouts around this which I adapt based on which joints I'm having problems with. The most frequent cardio session I  do is the 15 minute insanity workout by HASFIT. As the instructor says in the video, you can adjust this workout based on your level so it doesn't have to be insane if your fitness level isn't where you want it to be yet! With all new exercises, I start very cautiously with short durations, low weight and reps and see how my body reacts. From there I slowly increase the time, weight or reps each time to give myself a target. If you feel pain please stop. I do recommend that you see a specialist hypermobility physiotherapist to give you the best exercise programme based on your body.