Using a food processor, pulse the entire package of vanilla wafers until they are fine crumbs.

Add the 1 cup confectioners' sugar, 2 tablespoons cocoa powder, and corn syrup and pulse until combined. Scrape down the sides of the bowl as needed.

With the food processor running, slowly drizzle the rum through the chute of the mixture until well combined. If the mixture doesn't hold together when you pinch it, add more rum, a teaspoon at a time, until the mixture easily forms a ball.

Using a teaspoon (or small cookie scoop), scoop the dough from the food processor and form the dough into balls.

Add a small amount of confectioners' sugar to a shallow bowl (and if desired a small amount of cocoa powder to another shallow bowl) and roll the balls into either the sugar or the cocoa powder until well coated.

Place the rum balls on a parchment-lined baking sheet and refrigerate for 2 hours. Transfer to an airtight storage container. Store in the refrigerator for up to a month or in the freezer for up to 3 months. Bring to room temperature before serving.