Place a slice of prosciutto on the work surface. Place a shrimp across one end of the slice and then roll the shrimp up in the prosciutto to enclose it completely. Trim any ragged edges and press the prosciutto along the seams to seal it around the shrimp. Repeat with the remaining shrimp and prosciutto. Place assembled shrimp in a large bowl.
Squeeze generous amounts of lemon juice over the shrimp. Add olive oil and sprinkle with kosher salt and a few grindes of the pepper mill. Carefully toss to coat.
Drain off the water from the bamboo skewers. Place a shrimp on a work surface curved side up and press down gently with one hand to flatten the shrimp into a straight line. While holding the shrimp down in this way, insert the tip of the skewer into its tail end and continue to push the skewer through the middle of the shrimp all along its length until the tip comes out the head end. This will keep the shrimp straight during cooking. Repeat with the remaining shrimp.
Place the shrimp skewers on a hot grill and cook, turning them frequently, until the prosciutto is crisply browned and the shrimp wrapped inside are plump and pink, 6 to 8 minutes.