Mix wafer crumbs, 1 cup powdered sugar, nuts, and cocoa evenly in a large bowl.
In a small bowl, whisk together the corn syrup and rum until well combined.
Stir liquids into dry ingredients with a wooden spoon or hands until moist and holding together when pressed.
Roll into 1-inch balls; dampen hands if sticky.
Place additional powdered sugar in a shallow bowl and roll each ball until well coated.
Store in an airtight container at room temperature for at least 24 hours before serving to allow flavors to meld. They'll keep for up to 3 weeks or can be frozen for up to 3 months.