For one thing, Zanji's effect only activates if there's another Six Samurai monster on the field. However, if there was another Six Samurai, Zanji's effect would NOT activate. Blast speher becomes an equip card, and Zanji's effect only destroys monsters. However, I'm not totally sure on this one, so you shouldn't use me as a reference for this case.
EDIT: I've found out the answer for sure this time. Zanji destroys a monster at the end of the damage step, but Blast Sphere becomes an equip card before damage calculation. Therefore, Zanji's effect would not activate in response to it attacking a facedown Blast Sphere.