Afraid that 'cheap' doesn't enter into it if you're going to make it safe. Do you have room (and money) for a dedicated marine propane locker with all the associated safety equipment (shutoff solenoid and I'm not sure what else)? Carrying bulk propane on a boat shouldn't be taken lightly.
I have an Origo 2 burner alcohol/electric cooktop that I use and like alot. Another alrernative might be a camp stove that uses the small propane canisters. I have a single-burner propane stove that I sometimes use in the cockpit. Only keep aboard as much propane as you need, and store the canisters in a ventilated area. Unscrew the cylinder from the stove when you aren't using it.
My .02