Heat oven to 325 degrees. Whisk sugar and flour in a bowl. Add egg whites, then butter; whisk until smooth.
Line baking sheet with nonstick baking mat; coat with cooking spray. Thinly spread batter onto prepared baking sheet to cover. Bake until edges begin to turn light golden brown, 10 to 12 minutes. Immediately remove from oven; place sheet on a wire rack. Working quickly and carefully, cut shapes into cookie with cutter. If it becomes too hard to cut, return baking sheet to the oven for about 30 seconds until it becomes more pliable. Once cookie is filled with cut-out shapes, return to oven, and bake until most of cookie is golden brown, 5 to 7 minutes more.
Remove from oven; transfer individual cookies to a tray. To shape some of the cookies, mold into a cuplike shape, and set in a small shallow bowl to cool. Store in an airtight container up to 2 days.
Shortly before serving, stir a small drop of food coloring into melted white chocolate to tint. Dip each cookie into tinted chocolate using a chocolate fork. Place on a piece of acetate so chocolate stays smooth; transfer to refrigerator to set for about 30 minutes.
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