Yuta was a few feet away from Chorgan and only had to touch him briefly to kill him. For all intents and purposes she was holding a gun to his head. He could have tried to overpower her, but probably wouldn't have gotten to her in time. He could have aimed for her legs or gone for a sustained shot, but no guarantee then she would not somehow manage to touch him.
When innocent lives are in imminent danger you don't mess around.