Not sure if you can reshoot, but I have a makeshift solution. Instead of fixing it in post, how about placing rare earth magnets inside a hollowed out mouse and another one under the table. You can then move them around in a more realistic manner and without strings.
Since your hand would be moving the magnet under the table, it would be out of view and your mouse would follow the magnet under the table.
I am a magician as well as videographer and I always try and do special effects in “the real world” as much as possible. I just think that CG is good, but not good enough yet. The latest Star Wars flicks are a good example. Back in the “old days” models were used instead of CG. It looked better in my mind because the ships were ‘real.’ Just my 2 cents on that matter.
Warm regards,
Scott