Beat butter and shortening in a large bowl at medium speed with an electric mixer until fluffy; add egg, beating until blended.
Combine cookie mix and cocoa; gradually add to butter mixture, beating well. Shape dough into 1" balls. Place balls 2" apart on ungreased baking sheets.
Bake at 375° for 8 to 10 minutes. Cool 2 minutes. Gently press 1 cherry candy in center of each cookie. Cool completely on baking sheets; transfer to wire racks.
Combine powdered sugar and liqueur in a small bowl, stirring until smooth. (Glaze should be thick, yet easy to drizzle.) Place glaze in a small zip-top plastic bag. Snip a tiny hole in 1 corner of bag. Drizzle glaze over cookies. Let stand until set.
Note: Depending on the size candy box you buy, you may need two boxes for these cookies.