have not been given the ok for weights yet but still do rehab 30min each morning. Swimming has been great  swim hour each day but only aloud to do free and back untill scar tissue settles down still can not bend knee fully docter says it will take time how long did it take you to get a good movement range.
The exercises you are cleared to do are more than enough especially swimming. You will have to do a really good job of eating cleanly and counting calories. I presume that you can eventually build up your swimming and walking to decent distances. Can you lift weights? That is even better for fat loss. Diet is key here. If you can lift weights the circuit routine here is a good starting place. I don't have any comment on the lifting exercise that involve the knee except to say that if squatting is on your okay list, it opens up a world of possibilities for leg exercises.

I had rotator cuff surgery 8 years ago and during recovery, I crunched my ass off and did everything else that didn't involve my shoulders.