Whisk mayonnaise, lemon juice, garlic, 1/2 teaspoon cayenne and mustard in small bowl to blend. (Can be made 1 day ahead. Cover tightly with plastic wrap; refrigerate.)
Pour enough oil into heavy large pot to reach depth of 2 inches; heat to 375°F. Mix cornmeal, salt and 1/2 teaspoon cayenne in medium bowl. Add shrimp to bowl; toss to coat. Working in batches, add shrimp to hot oil and deep-fry until shrimp are golden and opaque in center, about 1 1/2 minutes. Using slotted spoon, transfer shrimp to paper towels to drain.
Place aioli in center of platter; surround with shrimp and serve.
