Combine mint leaves, sugar, and shallot in a bowl; pound with a spoon to crush coarsely. Whisk rum and 1/4 cup lime juice into mint mixture to make a marinade. Stir lime zest into the marinade; season with salt and black pepper.
Pour marinade into a resealable plastic bag. Add the shrimp, coat with the marinade, squeeze out excess air, and seal the bag. Marinate at room temperature 15 to 20 minutes.
Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Remove shrimp from marinade and thread onto 6 bamboo or metal skewers, all facing the same way. Discard marinade.
Cook the skewers on the preheated grill, turning frequently until nicely browned on all sides, and the meat is no longer pink in the center, about 5 minutes. Drizzle 2 tablespoons fresh lime juice over the skewers to serve.