Preheat an outdoor grill, indoor griddle or grill pan to medium-high heat. Dress the shrimp lightly in EVOO, then season with the smoked paprika, onion powder and garlic powder; season with salt and pepper. Thread the shrimp onto metal skewers. Grill until pink and firm, about 2 minutes on each side. Douse with the lime juice, then remove the shrimp from the skewers and chop; sprinkle with the cilantro or parsley. Dress the avocado with the lemon juice.
Build the quesadillas on the tortillas in assembly line fashion: On one half of each tortilla, arrange the shrimp, tomatoes, scallions, avocado and cheese. Fold over the other tortilla half, then spray lightly with cooking spray. Grill, turning once, until crisp and the cheese has melted, about 5 minutes. Cut into wedges and serve.