Place the shrimp in a large, 1-gallon re-sealable food storage plastic bag. Place the rest of the ingredients (coconut milk through salt) in a non-reactive medium bowl and whisk to combine. Pour the marinade over the shrimp and seal in the bag. Allow to marinate at room temperature for 30 minutes, turning the bag occasionally to ensure even marinating. Soak bamboo skewers in warm water while you marinade the shrimp.
Preheat the grill to medium-high. Remove the shrimp from the marinade and skewer 4 per skewer and set aside. Brush the grill lightly with a bit of vegetable oil and place the shrimp on the grill. Cook the shrimp for 3 minutes, basting with the marinade as it cooks, then turn and cook for an additional 3 minutes, while basting, on the second side. Serve while hot.