Beat butter and shortening at medium speed until fluffy; add sugar and cream until fluffy.
Combine coconut water and milk. Stir together flour, baking powder and salt. Add butter mixture alternately with milk mixture. Begin and end with flour mixture. Add lime zest and juice.
Beat egg whites at medium speed with an electric mixer until stiff peaks form; fold in to batter.
Pour batter into a 9x13 pan.
Bake at 350 degrees 25 to 30 minutes or until wooden skewer inserted in center comes out clean.
Cool in pan 10 minutes.
Remove cake from pan onto a wire rack. Cool completely.
Whisk 3/4 c milk and 1/4 c cornstarch in a 3 quart heavy saucepan, whisking until cornstarch dissolves. Add sweetened condensed milk and eggs until blended. Whisk in lime juice.
Boil 1 minute, whisking constantly or until mixture thickens. Remove from heat. Whisk in butter and lime zest. Pour filling into a bowl and place bowl in a larger bowl filled with ice. Stir until cold about 10 minutes.
Cut cake horizontally into 2 equal parts. Spread lime filling on bottom layer. Replace top. Spread Whipped Topping over entire cake and sprinkle coconut over topping.
For Whipped Topping:
In a large bowl, whip cream until stiff peaks are just about to form. Beat in vanilla and sugar until peaks form. Stop. Do not over-beat, cream will become lumpy and butter-like. Sprinkle 1/4 c flaked coconut on top.