Something I have done many times and have found to be very helpful is to tie your reins (as Lucy Conway has said) and stick your arms out to the side like an airplane for balance over jumps. A good way to practise is to set up a gym line with 3-4 jumps and a stride or two before release your reins and keep your arms out until the horse lands at the other end of your gym line. Not only does this require you to rely on your leg and seat instead, but forces you to use your body to balance yourself (this is also a great way to practise equitation over fences).
I do when jumping no hands which is a bit of a laugh to and for core exercises I do a Plank for 4 mins and do 50-70leg lifts and 50-70 sit ups and 30-50 crunches.
Hope this helps
Tie up your reins and when you jump put your hands on your head! It’s attually really fun!!