Why do sword owners tap them with a fluffy ball on a stick? In many shows characters poke their Japanese swords with a soft-looking ball on a stick. It seems that swordsmen in real life did that too. What's the purpose of that? Here's one example from Shaman king E02:
This “fluffy ball” is a standard part of any sword care kit (see the red ball in the picture below). It contains some sort of powder ‒ I believe chalk ‒ that is used gather and bind any fluids on the sword before oiling it again. (That powder acts sort of like a sponge.)

When cleaning your sword you will usually use clean water to remove any big pieces of dirt, then distribute this chalk powder all over your sword by “poking” the “fluffy ball” on the sword and then use a clean cloth to wipe the blade clean before putting the oil on it and distributing it evenly.