I realize Poe wrote fiction but we all write what we know. While the story is fiction he wouldn't put anything into it that his readers would object to. In the story the sailors also used "Bowie Knives". I had to check the history of the knives. The story was written shortly after the fight that made Jim Bowie famous. It made perfect sense for him to use it because his readers would see it as recognizable.

I believe these "pocket handkerchiefs" are not what we are used to. They were probably squares of trade cloth used to get the attentions of the island girls.