Beat butter and shortening until fluffy; add sugars, beating well. Beat in eggs, oil and vanilla. In a separate bowl, combine flour and remaining ingredients except candy coating, candies and sticks. Cover and chill 2 hours. Shape dough into 1 1/2 inch balls. Place 2 inches apart on ungreased baking sheets. Insert a stick about one inch into each ball. Bake at 350 degrees for 10 to 11 minutes, until set. Let cool 2 minutes on baking sheets; cool completely on wire racks. Coat with melted candy coating. Decorate with candies. Pipe whiskers with white candy coating.
Here's a quick way to candy coat your cookie pops: Place a cooling rack up high supported between 2 cake mix boxes. Cover with waxed paper. After dipping the cookie pops, poke the stick through the waxed paper on the rack and let cool.