Good ideas. I think pivoting with the bag would hurt, but it's worth a try.
After my knee surgery I spent A LOT of time swimming. If you get a buoy (lots of pools have them for you to use)for between your thighs then you won't kick and your legs will float.
I agree with with Phate on the swimming recommendation if you can get to a pool. Great full body cardio that is very low impact to bones and joints.
We have just had a thread on this topic