Using a blender or food processor pulse together lime juice, salt, thyme, pepper, garlic, and peppers until creamy. Pour marinade in a large resealable bag and place fish in marinade. Seal bag and let rest in the refrigerator 2 to 4 hours, flipping bag a few times.
Using a blender or food processor pulse together cilantro, lime juice, water, olive oil, caper, vinegar, peppers, salt, pepper, garlic, and shallot until creamy.
Take fish out of bag and lay on hot grill greased with cooking spray. Cook 3 minutes per side, fish should flake easily when finished. Spoon caper sauce on top or serve on side.