Crumble the completely cooled red velvet cake into a large mixing bowl until it resembles fine crumbs with no large pieces.
Add the entire can of cream cheese frosting to the bowl and stir vigorously with a wooden spoon until the mixture is completely combined and holds together when pressed, forming a thick, paste-like dough.
Roll the cake mixture into 48 tightly packed, 1-inch balls and place them on a parchment-lined baking sheet. Chill the balls in the refrigerator for at least 2 hours until very firm.
Melt the white chocolate candy melts and vegetable shortening together in a microwave-safe bowl, heating in 30-second intervals and stirring between each, until the mixture is completely smooth and fluid.
Insert a lollipop stick about halfway into each chilled cake ball, then dip it completely into the melted chocolate, swirling gently to coat. Allow the excess chocolate to drip off.
Immediately decorate with sprinkles before the coating sets. Stand the cake pops upright in a styrofoam block to dry completely, about 30 minutes.