You could definitely replace the handle as that’s attached on the outside. Before doing anything dramatic, I’d shoot everything with some PB Blaster and let it soak in that. You could even remove the hose (with the valve closed), suck the water out, and shoot some down there.
If that doesn’t work, I think your only next step would be to deal with this during your next haulout. You certainly cannot open the valve with no hose while it’s in the water.
My boat is coming out tomorrow. Other than paint, the main reason is the port engine seacock is stuck open and I don't want to start beating on it in the water. Imagine breaking that off. A 4" hole in the bottom of the boat would not be stoppable. The least I would do is put it in the straps of the lift and then start working o it. If it is an easy fix you are usually only charged for the travel lift time and not blocking.