Step 1: Prepare the shrimp and marinade: Rinse the shrimp under cold running water, then drain them and blot dry with paper towels.
Step 2: Combine the scallions, ginger, garlic, Scotch bonnet, soy sauce, 2 tablespoons of honey, and the peanut oil in a large bowl and whisk to mix. Add the shrimp, tossing to coat. Let the shrimp marinate in the refrigerator, covered, for 1 hour.
Step 3: While the shrimp marinates, prepare the sugarcane skewers: Using a long sharp knife, cut the sugarcane swizzle sticks into 3-inch lengths, slicing them sharply on the diagonal to make a sharp point. You will need one skewer for each shrimp.
Step 4: Make the rum glaze: Combine the 1/3 cup of rum, the tomato paste, brown sugar, 1 tablespoon of honey, lime juice, Worcestershire sauce, mustard, Tabasco sauce, allspice, and cloves in a small heavy saucepan and bring to a boil over medium-high heat, stirring until blended and the sugar melts. Reduce the heat to medium and let simmer until a syrupy glaze forms, 3 to 5 minutes. Remove the rum glaze from the heat, stir in the remaining 1 tablespoon of rum, and season with salt and pepper to taste.
Step 5: Remove the shrimp from the marinade and discard the marinade. Using a metal skewer, make a “starter” hole in each shrimp. Thread one shrimp on each sugarcane skewer, starting with the pointed end.
Step 6: Set up the grill for direct grilling and preheat to high.
Step 7: When ready to cook, brush and oil the grill grate. Arrange the shrimp on the hot grate and grill, turning with tongs, until nicely browned on the outside and firm and pink inside, about 2 minutes per side. Brush the shrimp with the rum glaze as they cook.
Step 8: Transfer the shrimp to serving plates or a platter. Spoon any remaining rum glaze over the shrimp and serve at once.