Krampus has his birch switches and (in some some stories) a whip, but don't forget Knecht Ruprecht (aka Hans Ruprecht, Rumpknecht, and Rû Clås (Rough Nicholas)). Knecht Ruprecht is Father Christmas' manservent who goes along with Santa "threatening to thrash or abduct disobedient children."
What does Knecht Ruprecht do with naughty children?
" he hits the children with his bag of ashes... He also reported to give naughty children a switch (stick) in their shoes for their parents to hit them with"
Then there was Belsnickel, who handed out "good boy and girl spankings" with a hazel switch - swinging it hard enough to leave marks so you have proof of the Christmas visit.
"Children then not only saw the mysterious person, but felt him or rather his stripes upon their backs with his switch. ... He or she would be equipped with an ample sack about the shoulders filled with cakes, nuts, and fruits, and a long hazel switch which was supposed to have some kind of a charm in it as well as a sting. One would scatter the goodies upon the floor, and then the scramble would begin by the delighted children, and the other hand would ply the switch upon the backs of the excited youngsters - who would not show a wince, but had it been parental discipline there would have been screams to reach a long distance."
One of these days I'll write a story about how these neglected companions of Santa try to modernize their images, but I haven't had the chance to write a Christmas story for the last few years... Maybe I should start on in Rebury this year... Until then I did write one story about a girl getting "joke gifts" of spanking instruments...
https://upload.wikimedia.org/wikipedia/commons/e/e2/Gruss_vom_Krampus.jpg