In a blender or food processor, process the olive oil, sesame oil, lemon juice, onion, garlic, ginger, cilantro, paprika, salt, and pepper until smooth. Reserve a small amount for basting. Pour the remaining mixture into a dish, add shrimp, and stir to coat. Cover, and refrigerate for 2 hours.
Preheat grill for medium heat. Thread shrimp onto skewers, piercing once near the tail and once near the head. Discard marinade.
Lightly oil grill grate. Grill shrimp for 2 to 3 minutes per side, or until opaque. Baste with reserved sauce while cooking.
