Combine mayonnaise, crab, garlic, salt, cayenne, Worcestershire sauce, lemon juice, and tarragon in a bowl for the crab aioli. Stir to combine and refrigerate until needed.
Remove tails from shrimp and keep chilled until ready to use.
Preheat the oven to 400 degrees F (200 degrees C).
Whisk buttermilk, hot sauce, chipotle pepper, cayenne, black pepper, and salt together in a bowl.
Mix flour, cornmeal, paprika, and salt together in a shallow dish for the breading.
Slice partway through each sandwich roll, splitting it open. Scoop out some bread from the top to make room for the filling.
Toast rolls in the preheated oven until crisp, 7 to 10 minutes.
Soak shrimp in the buttermilk mixture for about 5 minutes.
Heat oil in a pan over medium-high heat. Spread crab aioli generously over both sides of each roll; top with sliced lettuce.
Toss shrimp in the breading to coat; shake off any excess. Fry shrimp in the hot oil until golden brown and crispy, about 2 minutes per side. Drain on a paper towel-lined plate and immediately transfer shrimp onto the rolls. Sprinkle cayenne pepper on top.