Prepare a gas or charcoal grill for high heat (you can hold your hand 1 to 2 in. above cooking grate only 1 to 2 seconds). Meanwhile, put shrimp in a 1-gal. resealable plastic bag and pour in marinade. Seal and marinate at room temperature 15 to 20 minutes.
Remove shrimp, reserving marinade. Thread shrimp onto 6 or 7 (10- to 14-in.) metal or bamboo skewers.
Arrange shrimp on grill and baste with marinade (dab some mint and shallot onto shrimp); close lid. Cook until shrimp are just beginning to brown, 1 to 2 minutes. Turn shrimp over, baste again, and close lid. Cook 1 to 2 minutes until browned but still moist in center (cut to check). Transfer shrimp to a platter, drizzle with lime juice, and garnish with mint sprigs.
Note: Nutritional analysis is per serving.
Don't marinate for more than the recommended time or the rum and lime juice will "cook" the shrimp and ruin their texture.