In a small bowl, crush the garlic with the salt. Mix in cayenne pepper and paprika, and then stir in olive oil and lemon juice to form a paste. In a large bowl, toss shrimp with garlic paste until evenly coated.
Lightly oil grill grate. Cook shrimp for 2 to 3 minutes per side, or until opaque. Transfer to a serving dish, garnish with lemon wedges, and serve.