Coat and fry the shrimp
Clip a deep fat/candy thermometer to the side of a 12-inch cast-iron skillet and add enough oil to measure 3/4 inch deep. Heat to 360°F over medium heat.
Meanwhile, in a medium bowl, whisk together the flour, sugar, Cajun seasoning, and 1/2 tsp. salt; then slowly whisk in the beer and hot sauce to make a smooth batter. In a shallow bowl, combine the panko and shredded coconut.
Holding a shrimp by its tail, dip it into the batter, letting any excess drip off, then dredge it in the panko mixture, pressing and rolling it several times to coat well. Transfer to a plate. Repeat with the remaining shrimp.
Fry the shrimp in the hot oil, turning once with tongs, until golden-brown, about 2 minutes. If necessary, adjust the heat to maintain the oil at 360°F. Transfer the shrimp with a slotted spoon to a plate lined with paper towels to drain briefly.
Serve the shrimp with the rémoulade sauce.