No. I hate this suggestion. I love Kirk brashly saying "hit em with everything we got. Sure, Trek is all about optimism and hating your enemies, but this is also Krik, and you really want him to be as bad ass a character as when he starte d(even considering that he did try to offer to help). To do this suggestion would castrate the whole film.
I don't think that showing Kirk acting in self-defence as opposed to summarily executing his foe would castrate the film. If you think that making Kirk a 'bad ass' means he has to kill people when it's unnecessary then I'd say you've missed the point of Trek! Kirk's 'bad ass' reputation should come from his (often ludicrous) ability to take calculated risks and win.
In a modern context, if an armed suspect puts down his gun and a police officer aware of that fact then shoots and kills him, the officer would be investigated and probably punished unless he could show sufficient reason why he genuinely believed his suspect still posed a threat.
In STIII Kirk didn't kill Maltz even though Maltz wanted him to. I'd have been appalled if he had done so.