Thankfully, the episode steered clear of Kirk single-handedly deciding the course of a war with a rival culture. He was, after all, not a diplomat but a soldier. It would be a sorry Federation indeed where one person would be burdened with all the tasks currently split across tens of thousands of professionals of various fields!
Also, I definitely think "We have the right to wage war!" is part of the hard, solid core of the person called James T. Kirk. We never got a reason to think differently. If Kirk negotiates, it is not for avoiding conflict - it is for gaining the upper hand. Kirk decides who his enemies are, and then defeats those; there is no attempt at making friends out of enemies in any of the episodes or movies.
That doesn't mean Kirk wouldn't be a compassionate, moderate and lenient man by our standards. When he gets angry at a species, he goes to war against Klingons - with phasers on stun. When he gets really mad at a person, he blasts Khan's starship to bits - and then offers to beam him to safety. When his very son is murdered, he mows down all the murderer's henchmen - and then offers a helping hand to the chief villain. But that's merely the new definition of a hardass conservative for the 23rd century.