Even if you ignore the moral implications of killing the orcs in general plus the moral issue of murder without trial versus execution, at the very least there is the point that his actions caused the death of a few dwarven guards, who were NOT about to die anyway.
They should just leave.
Later, they might encounter each other again since it's possible for two adventurers to take the same quest (even likely in the world of D&D), but they should leave, and under no circumstances allow Ardon to lead.
At BEST, they should treat him as a battle advisor.