Heat oven to 350°F. In large bowl, break up cookie dough. Stir or knead in 1/4 cup flour until well blended. Remove half the dough, and refrigerate remaining dough until needed.
Sprinkle 2 tablespoons flour onto work surface. With rolling pin, roll dough 1/4 inch thick. With 3 1/2-inch guitar-shaped cookie cutter, cut out guitar shapes. On ungreased cookie sheets, place shapes 2 inches apart. Repeat with remaining dough and flour.
Bake 7 to 11 minutes or until light golden brown. Cool 1 minute; remove from cookie sheets to cooling racks. Cool completely, about 15 minutes.
In small bowl, mix powdered sugar, corn syrup and enough milk until smooth and spreadable. Stir in food color. Frost and decorate cookies with remaining ingredients as desired.