They say that the hooks will rust and fall out. Research does not tend to prove this. Hooks are made of high quality steel and even in salt water, they will last for months/years. Research has shown that the presence of a hook increases the chances of infection and raises the mortality rate.
If you must cut the line and stay safe, then stay safe and cut!
If you want to de-hook, begin with a tail-rope to get proper and safe control of the fish. I like S-dehookers, but begin with a good pair of pliers and discover what works be for you.
Sharks are my favorite fish to catch. Have fun!