Kathryn wouldn't have any problem at all with killing Edith. The basic premise of "City on the Edge of Forever" is "would Kirk give up the universe he knows (and everyone in it) for the life of the woman he loves"?What would she find harder, killing Hitler or not saving Edith Keeler?
Kathryn isn't in love with Edith, so no problem.
He couldn't stop her from agreeing to destroy Equinox for the subspace beasties depiste protesting that ,murdering starfleet officers is naughty and that relieving them of their freedom is adequate punishment.
Do the words "Please don't kill me?" bring a tear to anyones eyes? And mark me she would held him down and done exactly the same to him at the conclusion of Riddles if he even thought about resisting her insistence on the solid state of right and wrong.
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