Maybe a bee smoker?
Can produce lots of smoke from cardboard, though they can get quite hot.
I'm a beekeeper, so for once I might be able to offer some advice on this forum :)
When smoking bees, you want the smoke to be cool, white and thick, and easy to control with the bellows. We use fuels that smolder slowly and pack the smoker so that it will last a long time, not burning too fast and not dying out when you need it the most (which of course it does). When resting, it should only release a whisper of smoke, and a few puffs should produce a nice cloud of smoke quickly.
I test the smoke on the back of my hand before using it on the stinging insects, they do not like hot smoke in their face. The smoker itself does get very hot, so one should be careful not to put it down where it can burn or melt stuff. You shouldn't see sparks, but you might if you haven't loaded it correctly. A great trick is to stuff some green grass in the spout, acting as a filter.
Packing, lighting and keeping a smoker lit is an artform that took me years to master. Everybody has their techniques and favorite fuels. My favorites are old pine cones, grey egg cartons and beech wood chips. The latter is the most luxurious – it smells great and lasts a long time, being the very same stuff they use to smoke meats.
If I had to pick one, I'd go with egg cartons. I always carry it as a backup and use it to light the smoker. It might work on its own, eg. in a saucepan, if you want to give it a try. I wouldn't use cardboard.
With all that said, why not invite a beekeeper on board? If I were in the area, I'd be happy to smoke your junk sails… Now that's a weird sentence.
I agree with Jan, I would let the coast guard know you're not on fire, because it might look that way.