In a small bowl whisk together lime juice, olive oil, garlic powder, paprika, salt and pepper. Add the shrimp to the bowl and toss to coat. Set aside to marinate for 15-30 minutes.
Meanwhile, to make the herbed yogurt sauce, place the parsley in a food processor and pulse to roughly chop the parsley. Add the yogurt, garlic clove, lime juice and salt/pepper and blend until well combined and smooth.
While the food processor is running, slowly pour in the olive oil and allow it to emulsify the sauce, scraping down the sides of the food processor as necessary.
Preheat the grill to medium heat. Thread the shrimp on skewers and place on the grill. Grill on each side for 2-3 minutes or until no longer pink.
Remove the skewers from the grill and serve immediately with the herbed yogurt sauce.