Peel shrimp, leaving tails intact, and devein, if desired.
Combine crushed crackers, flour, 1/2 teaspoon pepper, and salt in a shallow dish. Stir together buttermilk, hot sauce, egg, and remaining 1/4 teaspoon pepper in a bowl until blended. Dip shrimp in buttermilk mixture; dredge in cracker mixture.
Pour oil to a depth of 2 1/2 inches into a large, deep cast-iron or heavy-duty skillet; heat to 375°. Fry shrimp, in batches, 1 to 2 minutes or until golden; drain on wire racks over paper towels.