1. Combine first 5 ingredients in a small bowl. Reserve 3/4 cup juice mixture. Stir carrot and chile into remaining 1/2 cup juice mixture, and set aside.
2. Peel shrimp, leaving tails intact. Starting at tail end, butterfly each shrimp, cutting to, but not through, backside of shrimp. Combine reserved 3/4 cup juice mixture and shrimp in a large bowl, tossing to coat; cover and marinate in refrigerator 1 hour, tossing occasionally. Remove shrimp from bowl, reserving marinade.
3. Prepare grill for medium-high heat.
4. Place reserved marinade in a small saucepan; bring to a boil. Reduce heat, and simmer 5 minutes. Cool slightly.
5. Thread 3 shrimp onto each of 12 (10-inch) skewers. Place shrimp on a grill rack coated with cooking spray. Grill shrimp 2 1/2 minutes on each side or until done, basting frequently with cooked marinade.
6. Cut 3 avocado halves in half lengthwise; peel and dice remaining avocado half. Brush cooked marinade over mango and avocado wedges; coat with cooking spray. Arrange in a single layer on grill rack coated with cooking spray. Coat lime wedges with cooking spray; place on grill rack. Grill fruit 2 minutes on each side or until marked but not soft, basting frequently with marinade.
7. Place 1 lettuce leaf on each of 6 salad plates; top each leaf with 2 mango slices, 2 lime wedges, and 1 avocado wedge. Place 2 skewers on each plate; sprinkle evenly with diced avocado. Sprinkle with cilantro, if desired. Serve with carrot mixture.