Prepare a charcoal or gas grill for direct grilling over high heat and oil the rack if needed so the shrimp do not stick to the grill. A grill pan may be used if a grill isn't available.
Mix together the paprika, garlic, powder, lemon pepper, and salt in a small bowl. Coat the shrimp with the spice rub.
Place the shrimp in a grill basket or thread them on 2 parallel skewers that have been soaking in water for 30 minutes. Set aside.
Add butter, lemon zest, lemon juice, and cayenne pepper into a small saucepan.
Once the butter has melted whisk ingredients together. Pour 1/4 cup into a small bowl to use for basting the shrimp.
Grill the shrimp directly over high heat, turning once and basting once or twice with the lemon-garlic butter, until evenly pink and opaque throughout, 3-4 minutes on each side. Do not overcook.
Transfer the skewers to a platter. Pour the reserved lemon-garlic butter over the shrimp and serve immediately. Serves 4 for a main course and 8 for appetizers.