Thread the peeled and deveined shrimp onto skewers, leaving space between each piece for even cooking. Set aside.
In a small bowl, combine olive oil, black pepper, smoked paprika, and minced garlic. Brush this marinade evenly over both sides of the shrimp skewers.
Preheat the grill or grill pan to high heat until hot and slightly smoking, about 5 minutes. Oil the grill grates lightly to prevent sticking.
Place the shrimp skewers onto the hot grill. Cook for about 2-3 minutes per side, until the exterior is charred and smoky, and the shrimp turn opaque and firm. You should hear a hiss and see grill marks with a slight caramelization.
Remove the shrimp from the grill using tongs and transfer to a plate. Serve immediately with lemon wedges for squeezing, and observe the vibrant, slightly smoky appearance with crispy edges.