Pulse shrimp in a food processor 4 or 5 times or until chopped. Spoon into a medium bowl.
Melt butter in a small skillet over medium heat; add celery and onion, and sauté until tender. Add to shrimp in bowl; gently stir in 1 cup panko and next 6 ingredients. Shape mixture into 8 patties (about 1/3 cup each). Place remaining 1/2 cup panko in a shallow dish; dredge both sides of patties in panko. Place patties on an aluminum foil- or parchment-lined baking sheet; cover and chill 1 hour.
Fry patties in hot oil, in 2 batches, in a large skillet over medium-high heat 2 to 3 minutes on each side or until golden. Drain on paper towels.
Cut Chive Biscuits in half. Place 1/4 cup lettuce on bottom half of each biscuit; top with a dollop of Louis Dressing and 1 shrimp patty. Cover with top halves of biscuits.