Mix first 5 ingredients in food processor or blender. Process on high until pureed (mixture will not be smooth). Transfer to large food storage bag. Add thawed shrimp; seal bag. Massage bag to coat shrimp. Refrigerate 1 to 2 hours to marinate.
Heat grill. Thread shrimp and remaining ingredients on skewers. Grill 5 to 7 minutes until shrimp are opaque and cooked through, turning once or twice.
