1Grate 2 tablespoons peel from limes. Cut each lime in half crosswise; squeeze halves over small bowl to remove 6 tablespoons juice.
2Place melon cubes in 1-gallon resealable food-storage plastic bag. Sprinkle lime peel and pour lime juice over melon. Add sugar, rum and mint. Seal bag; turn to coat melon.
3Refrigerate at least 1 hour to blend flavors but no longer than 24 hours. To serve, thread 4 or 5 melon cubes on each skewer. Discard marinade.