Well, obviously a pirate would pick up stuff from different places, and of course it doesn't have to have the typical pirate sword, but I doubt a pirate would pick up a useless sword. Different swords have different purposes/uses, rapiers don't have slashing power, they were made pur puncturing the enemy, and you have to be trained to use that, what use would a pirate have for one? I would imagine a pirate would prefer a saber, or even a samurai sword, because then he can "swing it" at the enemies, and haven't you even seen a pirate grab on to a rope, then cut it somewhere below his hand and be pulled up to the other ship or something? hehe
About the rapier being "fancier", look at the picture I attached. number 363.1 (it apears twice) is a saber and it's all fancy. Notice how it has a thick curved blade, that's for slashing throats .

also, the gold teeth sounds like a good idea. Obviously he should also have some missing.