I would advise against one arm training with upperbody, as the muscles on one side of your body might be disproportionate in strength. For instance, a one armed dumbbell press will only workout one chest muscle. As far as specific bodyweight exercises, there aren't really many without use of a machine or a cable that work both sides of the body and that spare your arm. I can think of several exercises if you don't mind the muscle asymmetries but to hit both sided---
Swiss ball hamstring curl,
Swiss ball jacknife
, sled pulls with a strap around your waist
, squat jumps without weight.
Regular squats might be feasible if you have use of your hand for grip but it can still apply more than the recommended use of 5 to 10 pound weight restrictions doctor's usually give you. Again this isn't a bodyweight exercise
Crunches, decline crunches, Swiss ball crunches,
Crunch with rotation, or twist with a medicine ball
Several other ab exercises
Possibly pallov press?
Sprinting is also great for full leg development