Since the beginning, we see Yoroichi does not wield a Zanpakuto, but isn't it strange? Isn't she a Shinigami and the Zanpakuto is so important for them?
It's true that she has her own fighting style, but like Soi Fon, she has the same fighting style, but uses a Zanpakuto.
There was some flashback moments when we saw younger Yoroichi wielding a Zanpakuto:
I imagine she had Shikai/Bankai to become a Captain, so she should be stronger if she uses it in a fight. Maybe she has lost it or something?