Peel shrimp, leaving tails on; devein, if desired.
Dip shrimp in egg. Stir together breadcrumbs and coconut; dredge shrimp in mixture.
Pour oil into a Dutch oven; heat to 375°. Fry shrimp, in batches, over medium-high heat 2 minutes or until golden. Drain on paper towels.
Spoon Napa Cabbage Slaw evenly into 8 martini glasses. Top each with 3 fried shrimp. Garnish, if desired.