Keigo has a small amount of spiritual power, not enough to gain any unique abilities but enough to see and touch spirits. Like the rest of the people in the portion of the real Karakura Town that is in Soul Society, his physical body would have been transformed into a spirit body when the town was transferred to Soul Society (like was done when Uryu, Orihime, Sado, Ichigo & Yoruichi when they went to rescue Rukia in the Soul Society arc). Therefore he can pick up a zanpakuto (note: he can only use it as a normal sword - he cannot access its abilities).