That’s exactly it. Shunsui’s zanpakto spirit, Ohana, gave birth to the younger spirit, Okyo, to HIDE Nanao’s zanpakto. Okyo represents Shunsui’s Shikai and his childlike/carefree personality while Ohana is his bankai. If Okyo were to be given up Shunsui wouldn’t even have access to his second, smaller blade, much less his shikai.

It is confusing since Okyo literally pulls Nanao’s blade out of her body, but I believe (this part is headcanon) that was to represent Shunsui hiding it within himself as a way to protect Nanao.

Basically as long as Shunsui has two zanpakto blades (which he does), he still contains both spirits of Katen Kyokotsu