Building a cavalryman vs. building a charioteer

[whswhs]

A cavalryman has to both control the mount and wield the lance, bow, pistol, or whatever. But a chariot characteristically has two people: the driver and the shooter. Arjuna is making Bow rolls; Krishna is making Teamster rolls. It's rare for a chariot warrior to use a melee weapon; a chariot is primarily a shooting platform. So the rules you cite fail to apply on two grounds: That Arjuna isn't using a melee weapon, and that someone else is controlling his chariot for him.