Bring sugar and lime juice to a simmer in a small saucepan. Cook, stirring, until sugar dissolves, about 2 minutes. Remove from heat; stir in lime zest, chili paste and fish sauce. Season with salt.
Soak wooden skewers in water for 30 minutes.
Heat grill to high. Brush grates with oil. Thread 3 shrimp onto each skewer; season with salt. Divide sauce in half. Grill shrimp for 1 minute, brush with sauce, flip and repeat until opaque. Serve with extra sauce.