Finely chop shrimp by hand or in a food processor (do not puree). Transfer to a bowl and mix in the mayonnaise, egg, flour, lemon juice, green onion, garlic, salt and tabasco.
Spread the cornmeal on a plate. Dampen hands slightly with cold water and shape shrimp mixture into 4 balls. Set the balls on the cornmeal. Sprinkle the top and sides of each ball with cornmeal. Shape each ball into a 5" wide cake. Heat the oil in a large, non-stick skillet set over medium to medium-high heat. Cook the cakes 3 minutes per side, or until golden. Spread buns with tartar sauce. Set a lettuce leaf, and then a shrimp cake, on each bottom bun. Top with tomatoes, onion, pickles and top buns and serve.