It would of been easier if Spock just stunned both kirks as Garth would of just turned back into Garth and Kirk would of just been stunned
Getting hit with a phaser stun is probably like getting knocked out with a punch to the jaw. It would be a bigger deal when you can feel it than two-dimensional characters make it look. You don't want to stun the captain.
But if I wrote the scene, it would go like this:
SPOCK: "The captain and I had a working breakfast on Tuesday. Which crewman's name came up in regard to the disturbance on Deck 6?"
Before Kirk could answer, Garth would attack, and you'd still have your Big Fight.
That's why Nimoy was so unhappy with the scene. If Spock had half a brain, there would be any number of simple questions that only Kirk would know. It was just lazy writing, a disservice to the Spock character.