I wouldn't be surprised if these pirates were placed in this plaza to help keep kids busy while parents go shopping, and the look of the sculptures certainly falls into line with the pirate stereotype that one sees in the movies. But if you read the signs, they reference real pirates who were active in the area and it's pretty interesting if you can get past the cheesy and Disney-like appearance of the sculptures in the plaza.
One such pirate referenced on the sign was Jean-David Nau (illustrated below far left), better known as François L'Olonnais, who used French Cay (just south of Providenciales) as a hideout in the 1660's to wait for Spanish ships heading north towards the Bahamas. A little research of our own finds that L'Olonnais developed a reputation as an expert torturer, with techniques that included slicing portions of flesh off the victim with a sword or burning them alive. He also was known to use a technique called "woolding," in which a rope was tied around the victim's head and twisted tighter and tighter against the temples until the eyes burst out of their skull. I wonder if this pirate sculpture pictured to the right of L'Olonnais has a collection of eyeballs in his bucket?
I don't think the store owners who set up these pirates in their plaza want their customers to think too much about woolding as they're enjoying ice cream and shopping for souvenirs! The cute little "pirate boy" below right doesn’t look like he’s meant to intimidate anyone, let alone torture them.