Lightly coat onion slices with cooking spray. Place onion on grill rack coated with cooking spray; grill 4 minutes on each side. Cool and chop. Combine onion, mango, 1 teaspoon salt, and next 6 ingredients (through chiles) in a large bowl.
Combine oregano, remaining 1 1/4 teaspoons salt, pepper, shrimp, and garlic in a large bowl, and toss well. Thread shrimp onto skewers. Place skewers on grill rack coated with cooking spray; grill for 2 minutes on each side or until done.