Whisk 4 cups flour, club soda, 1 tablespoon plus 1 teaspoon baking powder, 1 tablespoon plus 1 teaspoon baking soda, and salt together in a large bowl to form a slightly lumpy batter.
Heat oil in a deep-fryer or large saucepan to 350 degrees F (175 degrees C).
Dust shrimp with remaining 2 cups flour. Dip shrimp into batter and place on a baking sheet to drain excess, 5 minutes.
Spread coconut out on a rimmed baking sheet. Roll battered shrimp in coconut.
Fry shrimp in hot oil in small batches, being careful not to crowd them, until they float to the top and turn golden brown, about 5 minutes. Drain on paper towels.
