In advance: Make wrapper ends. Add 1/2 teaspoon Gum-Tex to 6 oz. white fondant. Roll out 1/8 in. thick; cut two 1 x 3 in. long strips. Ruffle strips by folding in thirds; pinch end. Let dry on cornstarch-dusted cake board. Cut lollipop sticks to 2 1/2 in.; attach wrapper end to lollipop stick with fondant adhesive, leaving 1 1/2 in. extended. Let dry.
Ice cupcakes smooth. For mint spirals, roll out red fondant 1/8 in. thick. Cut three 1 1/2 x 1/8 in. strips and three 1 1/2 x 1/2 in. strips that taper to 1/4 in. wide. Position on cupcake in swirl formation.
Roll a 1/4 in. dot; attach at center with damp brush. Insert wrapper ends in cupcake.