Cut almost through each shrimp down its back, from neck to tail. Pull out and discard veins. Rinse shrimp and lay open, cut sides down, pressing to flatten. Lay butterflied shrimp in a container, about 9 by 13 inches.
Mix lime juice, garlic, butter, and hot sauce and pour half over the shrimp. If making ahead, cover and chill shrimp and reserved sauce up to 1 hour.
Lay shrimp, spread open, on a grill above a solid bed of hot coals or over high heat on a gas grill (you can hold your hand at grill level only 2 to 3 seconds). Close lid on gas grill. Cook, turning once, until shrimp are pink and opaque but still moist-looking in thickest part (cut to test), 5 to 7 minutes total. Transfer to a platter as cooked.
Combine shrimp marinade and reserved sauce and heat until boiling. Spoon sauce over grilled shrimp and add salt to taste.