Preheat oven to 350. Spray bottom of 13x9 pan with baking spray (with flour).
In a large bowl, beat cake mix, 1 1/3 cup of the coconut milk (set the remaining 1/3 cup aside for the frosting), water and egg whites on low speed 30 seconds; increase to medium speed and beat another 2 minutes. Stir in 1/2 cup of the shredded coconut until well combined; pour batter into prepared pan.
Bake about 30 minutes, remove from oven and let cool completely, about an hour.
Meanwhile, microwave white chips uncovered on high 30 seconds or until melted. Stir; if chips are not completely melted, microwave 15 seconds longer, then stir until all chips are melted. Stir in powdered sugar, butter, reserved coconut milk and the vanilla. Cover and refrigerate 30-60 minutes. If frosting becomes too firm to spread, microwave uncovered on high 10 to 15 seconds to soften; stir until smooth.
Spread frosting over cake; sprinkle with remaining coconut. Store loosely covered at room temperature.