Crumble the cooled red velvet cake into a large mixing bowl using your hands or a fork until it reaches a fine, uniform crumb consistency with no large chunks remaining.
Add the vanilla frosting to the cake crumbs. Use a spatula or your hands to fold and mix the frosting into the crumbs until a thick, dough-like mixture forms that holds its shape when squeezed.
Scoop approximately 1.5 tablespoons of the mixture and roll it firmly between your palms to create a smooth, 1.5-inch ball. Repeat with the remaining mixture to create approximately 24 cake balls.
Place the balls on a baking sheet lined with parchment paper and refrigerate for at least 30 minutes, or freeze for 15 minutes, until very firm but not frozen solid.
Place 1/2 cup of the white candy melts in a small microwave-safe bowl. Microwave in 30-second intervals, stirring in between, until completely smooth.
Dip the tip of one lollipop stick about 1/2 inch into the melted candy, then insert it halfway into a chilled cake ball. Repeat for all balls and return them to the refrigerator for 10 minutes to set the sticks.
Place the remaining white and red candy melts into two separate deep, narrow microwave-safe bowls. Add 1 tablespoon of vegetable shortening to each bowl to thin the coating for a smoother finish.
Microwave each bowl in 30-second increments, stirring well each time, until the coating is fluid and smooth.
Dip one cake pop vertically into the melted coating until the cake is completely submerged. Lift it out and gently tap the stick against the edge of the bowl to allow excess coating to drip off. Turn the stick slowly to ensure an even coat.
Immediately apply the festive sprinkles while the coating is still wet. Place the finished cake pops upright in a foam block or cake pop stand and allow them to dry completely for about 20 minutes before serving.