Position knife blade in food processor bowl; add first 6 ingredients. Process until blended; add rum and next 3 ingredients. Process until mixture holds together.
Shape into 1 1/4" balls. Roll balls in additional powdered sugar or gingersnap crumbs. Repeat rolling procedure.
Note: If Royal Rum Balls are made ahead, reroll balls in powdered sugar or gingersnap crumbs before serving to freshen the coating.