Preheat oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking pan with cooking spray.

Combine yellow cake mix, water, eggs, and vegetable oil in a large bowl; beat with an electric mixer until smooth, about 2 minutes. Fold in 1/2 cup shredded coconut. Pour into the prepared pan.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, 23 to 28 minutes.

Mix cream of coconut and white rum together in a bowl. Poke holes in the hot cake with the end of a wooden spoon; pour cream of coconut mixture evenly over the cake. Chill cake, 8 hours to overnight.

Mix remaining shredded coconut, crushed pineapple, and whipped topping together in a bowl. Spread evenly over the chilled cake. Chill for 1 hour before serving.