I carry the same thing with me on the catamaran that I do when I SCUBA dive, a pair of Sea Snip EMT scissors. They'll cut anything that can fit in their jaws (even a penny - I've tried) and they can be used with one hand. I gave up diving with the 'Rambo' dive knife long ago when I realized that the most dangerous thing in the water wasn't sharks, but rather stray monofillament fishing line.

Even if I had a ball-style trapeze harness, I would still carry the scissors on my PFD when I sail.