Heat oven to 180°C (170°C for dark or nonstick pans). Grease 2 (23cm) round cake pans with shortening; lightly flour.
In large bowl, beat cake mix, water, oil, buttermilk and egg whites with electric mixer on medium speed. Beat in melted white chocolate. Add about 20 drops blue food color to batter; mix well.
Scrape down bowl; mix again until no white streaks remain. Pour batter into pans. Bake as directed on cake mix box for 2 (23cm) rounds. Cool cakes completely before frosting.
Level each cake using large serrated knife or cake leveler. Cut each cake in half horizontally so there are four cake layers total. Reserve 110 grams frosting for later use; use remaining frosting to fill and frost entire cake.
Press coconut onto top and sides of cake. Transfer reserved frosting to decorating bag fitted with large star tip. Pipe rosettes around top edge of cake. Top each rosette with silver button. Store cake loosely covered.