Well, he could just walk up behind her.
When someone’s got a knife to your back or the threat of a knife to your back, the gun becomes a lot less relevant. A knife also lets him kill silently, while the gun makes a lot of noise. He can use the knife to disable the primary arm (or both arms) which she uses to hold her gun, and then the problem is solved. Miss the artery, go for the muscle or, better yet, a tendon.
Here’s your problem: just because he needs her alive doesn’t mean he needs her whole or in one piece. He just needs to make sure she doesn’t bleed out, and can’t retaliate. If he can’t harm her, well, that’s entirely different. But need? Needs her alive is code for, “what fun Mr. Tactical Baton and I will have!”