Kojo Kyoko, or rather, the Chen Yu behind her, prepared so-called enchanted wooden swords for Nanami and the other two young girls. These swords could harm ghosts and offered self-protection in the presence of such entities.
It wasn't that true swords couldn't be prepared, as Japan's laws regarding this matter weren't particularly stringent, but after all, those were true swords, and for three young girls, they were somewhat inappropriate.
So even though the plan was set for Kojo Kyoko to teach them swordsmanship, Chen Yu still didn't prepare true swords for them, but rather three wooden ones with special enchantments.
Of course, another reason for preparing wooden swords was that true swords were too heavy, and for young girls, they might not even be able to lift them. In contrast, wooden swords made of wood were much lighter and less cumbersome to use.