In a large bowl, combine 2 cups cool water, 1 tablespoon sea salt, lemon juice and halves, and ½ tablespoon cayenne pepper. Stir to dissolve the salt. Add ice cubes. Set ice bath aside.
Fill a medium saucepan with water and add 1 tablespoon sea salt, ½ tablespoon cayenne pepper, and bay leaf. Bring to a boil. Add shrimp and return to a boil. Immediately remove saucepan from heat and allow the shrimp to remain in the hot water until just cooked through, about 1 minute longer. Using a slotted spoon, transfer shrimp to ice bath until completely cool.
Meanwhile, stir to combine cream cheese, mayonnaise, lemon zest, parsley, minced green onion, and the remaining ¼ teaspoon salt and 1/8 teaspoon cayenne pepper in a medium bowl. Transfer the cream-cheese mixture to a piping bag fitted with ½-inch plain tip; refrigerate 15 minutes.
Remove shrimp from ice-water bath and pat dry with paper towels. Halve shrimp lengthwise; set aside.
Place crackers on a large platter. Top each cracker with a shrimp half and pipe each with about 1 teaspoon cream-cheese mixture. Garnish with celery, red bell pepper and sliced green onion.