- Combine molasses, ginger, rum, and lime zest in a medium bowl and stir to blend for about 20 seconds.
- Thread 4 shrimp onto each skewer.
- Preheat barbecue to medium-high or turn on the oven broiler.
- Sprinkle shrimp with sea salt. Place 3 Tbsp glaze in a bowl and set aside.
- Brush shrimp with some remaining glaze.
- Grill shrimp until just opaque in center, brushing occasionally with glaze, about 2 minutes per side.
- Drizzle with reserved glaze and serve.
DO AHEAD: Glaze and shrimp can be made 8 hours ahead.