I have probably 80 dives in Cozumel, maybe 12 in Roatan. More than some, fewer than most dedicated Carribbean divers. I carry a 3-4 inch stainless knife with a razor sharp edge in my utility pocket on my BP/w. I have never needed it during a dive. Nurse sharks are not an issue and we have seen one hammerhead off in the distance. Unless you were lionfish hunting, I don't think a shark would pay any attention to you. Even then, I have been concerned about a shark exactly zero times. Sharks don't like the taste of neoprene....
Knives are not allowed on the marine park in Coz. If you show up with a BFK Rambo special, if you can even get it into the country, I doubt your operator will let you dive with it. Mine stays in the pocket and I have never had to use it on a dive. I have had to use it to cut fruit on a surface interval.
Monofilament line is sometimes an issue in the park and I try and collect it (and other trash) when I find it on a dive. A DGX cutter recommended above is a better tool for that, I also carry the titanium trauma shears recommended here as well for one hand cutting if needed.
I do carry the knife on night dives for to stab people that shine their Mega Sun 9,000,000,000 lumen can lights in my eyes....sometimes even on the boat. It is the best tool for that. Highly effective. Turning off their air works too, just takes longer......
Seriously, the odds of needing a BFK for shark defense in the Carribbean are so small, you'd be better off being concerned about lightning, alien abduction, or a plane falling on you....possibly all at once. Worry about diving, buoyancy control, air consumption, trim, PROPER weighting, and learning to relax and enjoy the dive.
Keep in mind that there are dive shops in America, and the rest of the world, that do shark feeding dives where they take a crates of chunked fish and actually draw sharks in to feed them in front of the divers. Other than the guy that is actually feeding the shark, I'm not aware of a diver being bit on one of these trips...ever. In the case where his hand was bit, I think he held on to the fish too long. There are lots of YouTube videos on shark dives. If they wanted to eat you...they could.
I'm not trying to derail the topic about feeding dives, right or wrong, just pointing out that hundreds, if not thousands, of divers are around hungry sharks on a weekly basis. If it were a problem, we would know it.
For the record, I carry, consider myself hyper vigilant, and believe that my safety is my responsibility. Getting nibbled on by a shark while diving is not one of my concerns.
Safe travels,
Jay