Beat butter and shortening at medium speed of an electric mixer until creamy; gradually add sugar, beating well. Add egg, beating well. Stir in flavorings. Combine flour, baking powder, and salt; add to butter mixture, beating well. Remove half of dough from bowl. Add food coloring to dough in bowl, and mix until color is evenly distributed.
Working with half of each dough at a time, shape plain dough by teaspoonfuls into 4" ropes. (Cover remaining dough to prevent drying.) Repeat shaping with red dough. Place 1 red rope and 1 plain rope side by side; carefully twist together. Roll twisted ropes into 1 smooth rope; shape rope into a cane, and twist as needed to complete stripe design. Repeat with remaining dough. Chill 15 minutes.
Place cookie canes on ungreased cookie sheets. Bake at 375° for 8 minutes or just until cookies begin to brown. Cool slightly; carefully remove cookies to wire racks, using a wide spatula, and cool completely.