What strength training exercises are easiest on the hands?

For your lower body, you can barbell squats and barbell lunges (check Youtube for instructions).

Single-leg squats don't require much weight.

If you're strong enough - jumping lunges & jumping squats.

For your pushing muscles, you can do pushups on your fists (if you can't do them on the floor, put your fists on a couch or other raised object).

Pulling exercises should be fine with carpal tunnel, since you grip with your fingers. Good ones are the bent-over row (using 2 dumbbells or a barbell) and the standing cable row.

For shoulders, try front delt raises & side delt raises.

For lower back, Romanian deadlifts.

sit ups, squats, do cardio like jumping hacks or whatever. Strengthening arms is going to require grip. Just recover yourself first.