Rinse shrimp and drain. In a large bowl mix together salt and sugar. Add shrimp and stir to coat evenly. Cover bowl and chill at least 45 minutes or up to 2 hours.
If using wooden skewers, get them soaking in water for about 20 minutes. Prepare grill for direct-heat cooking.
Rinse salt and sugar from shrimp and pat dry. Thread shrimp in a C shape onto metal or wooden skewers. Lay the skewers in a rimmed pan. In a glass bowl, combine oil, lemon juice and garlic; Pour over shrimp and turn skewers to coat evenly. Let stand 5 to 10 minutes.
Lay skewers on grill over hot coals or high heat on a gas grill. Close lid on gas grill. Cook, turning once, until shrimp are bright pink on the outside and opaque but still moist-looking in center of thickest part, about 5 minutes.
Transfer skewers to a platter and serve with lemon wedges to squeeze juice over.