In a medium bowl, combine ginger, garlic, lime zest and juice, and coconut milk. Add shrimp, tossing to coat, and chill, covered, at least 1 hour and up to 1 day.
Meanwhile, soak skewers in water. Prepare a grill for high heat (450° to 550°; you can hold your hand 5 in. above cooking grate only 2 to 4 seconds). Push 2 or 3 shrimp onto each skewer in a "C" shape (through each end); cook, turning once, until flesh has just turned pink and is slightly charred, about 3 minutes on each side.
Arrange skewers on a serving platter and sprinkle evenly with salt, a squeeze of lime juice, and coconut. Serve with extra lime wedges on the side.
Note: Nutritional analysis is per 2-skewer serving.