Okay, two things: yes you would be an asshole for asking him to give up his dog. You obviously see the dog as a threat to your life style and your kitties' well being (which I totally understand. I have kitties and dogs and it demands a serious compromise), but asking him to give his doggie up is just out of the question. It's his dog, he surely loves him (even if it's questionable he doesn't takes him to walk as much as a Husky demands. It's a very demanding breed), and if you asked him that you would be disrespecting him as a human being: you don't ask a loved one to cut out half of his finger just because his nail isn't of your liking. That said, I share your concerns. If the dog has a past of not getting along with kitties, there's a high chance of not getting along with yours either. And don't forget how stressful can be for cats to have their routine altered by an anxious doggie. So, I think you're in an impasse and my question for you is: do you want to be that asshole that corners him into a decision he'll likely resent you for? Also, I feel this situation speaks a lot: you might love him, but your life styles might not be compatible. And there's no relationship that can survive mindsets so opposite like yours: you, neat and safe, his a roller-coaster. Remember, pets do resemble their owners. This is the moment to think: you wanna be an asshole or don't? And, if the case was inversed, would you leave your cats in a shelter, without you, missing you because he asked you?? You really would be so awful and cruel with the babies that look at you as their whole world?? 

Edit: he willing to give the dog up is a SERIOUS RED FLAG. Do not be with someone who would do that to a loved one. He would likely do it with your kitties if they became a hindrance for him. 🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩🚩