In a food processor, whirl coconut, chilies, anchovy paste, garlic, and lime juice until coconut and chilies are minced; scrape container sides frequently.
Rinse and drain shrimp. Thread onto 4 flat metal skewers (10 to 14 in.).
Place shrimp on a barbecue grill over a solid bed of medium-hot coals or on a gas grill set at medium-hot (you can hold your hand at grill level only 3 to 4 seconds); close lid on gas grill. Cook shrimp, turning once, until bright pink and opaque but still moist-looking in center of thickest part (cut to test), 3 to 5 minutes total.
Transfer shrimp to a platter. Serve with sambal paste to add to taste.