Bake the white cake according to package directions in a 9x13-inch pan. Let cool completely to room temperature, about 1 hour.
Crumble the cooled cake into a large bowl until you have fine crumbs with no large chunks remaining. Add the vanilla frosting, watermelon extract, and pink food coloring, mixing with your hands or a spatula until evenly combined and the mixture holds together when squeezed.
Roll the mixture into 24 evenly-sized balls (about 1.5 tablespoons each) and place them on a parchment-lined baking sheet. Press 3-4 mini chocolate chips into each ball if using, arranging them like watermelon seeds.
Refrigerate the cake balls for at least 2 hours or freeze for 30 minutes until very firm.
Melt the white candy melts according to package directions. Dip the tip of each lollipop stick about 1/2 inch into the melted coating, then insert it halfway into a chilled cake ball. Return to the fridge for 5 minutes to set the stick.
Working one at a time, dip each cake pop into the melted coating, covering completely. Gently tap your wrist to remove excess coating, allowing it to drip back into the bowl.
Stand the coated pops upright in a styrofoam block or upside-down colander. Let the coating set completely at room temperature for 30 minutes, or refrigerate for 10 minutes to speed up the process.