Combine first 8 ingredients in a large bowl; set 1 tablespoon of mixture aside. Add rice and next 4 ingredients to remaining juice mixture. Stir well; set aside.
Peel and devein shrimp. Place shrimp on rack of a broiler pan coated with cooking spray, and brush with reserved 1 tablespoon lime juice mixture. Broil 5 1/2 inches from heat (with electric oven door partially opened) 2 minutes on each side or until shrimp turn pink. Add shrimp to rice mixture, and stir. Serve salad immediately, or cover and chill.