Peel and devein shrimp; place in a heavy-duty, zip-top plastic bag. Combine 1 tablespoon lime juice and next 4 ingredients, and pour over shrimp. Seal bag; shake gently. Marinate in refrigerator 2 hours.
Place pepper, skin side up, on a baking sheet; flatten with palm of hand. Broil 5 1/2 inches from heat (with electric oven door partially opened) 10 minutes or until charred. Place in ice water until cool. Remove from water; peel and discard skin. Coarsely chop pepper; place in container of an electric blender. Coarsely chop tomatillos. Add tomatillos, remaining lime juice, avocado, and next 3 ingredients to blender; cover and process until smooth. Chill.
Remove shrimp from marinade; discard marinade. Thread shrimp onto four 8-inch skewers. Coat grill rack with cooking spray; place on grill over medium-hot coals (350° to 400°). Place shrimp on rack; grill, covered, 3 to 4 minutes on each side or until done. Remove shrimp from skewers, and place on serving plates. Serve with tomatillo mixture.