Bake the cake in a 9x13 inch pan according to package instructions and allow to cool completely to room temperature.
Crumble the cake into a large mixing bowl using a fork or hands until only fine crumbs remain.
Incorporate the vanilla frosting into the crumbs, mixing until the texture resembles moist dough that holds its shape when squeezed.
Form the mixture into 1.5-inch spheres and place them on a parchment-lined baking sheet.
Chill the cake balls in the refrigerator for 1 hour or the freezer for 20 minutes to firm up.
Melt the candy wafers and shortening in a deep microwave-safe bowl in 30-second intervals, stirring until smooth.
Dip the end of a lollipop stick into the melted candy and insert it halfway into a chilled cake ball.
Submerge the entire cake ball into the melted candy, lift out, and gently tap the stick against the bowl rim to remove excess coating.
Apply shamrock sprinkles while the coating is still wet and place the stick upright in a styrofoam block to set for 15 minutes.