In a large mixing bowl, beat with a hand mixer the sugar cookie mix, butter, egg white, and 3 tablespoons strawberry daiquiri mix until all the ingredients are well incorporated and a dough is formed. Using a small ice cream scoop or tablespoon measure, drop the dough out in cherry size rounds onto a baking sheet. Bake until puffed, 7 to 9 minutes. Allow to cool slightly on the pan before transferring to a wire cooling rack to cool completely.
In a small bowl, combine the powdered sugar with the remaining 2 tablespoons strawberry daiquiri mix and whisk until blended. The filling should have a thick consistency, but if it is too dry add a teaspoon or 2 of the daiquiri mix until the filling comes together. Spread a teaspoon of filling on the flat side of 1 of the cookies and sandwich with a second. Repeat with the remaining cookies and filling. Allow the filling to set before packaging.