"Some other man's dogs" ??
No, they are YOUR dogs and part of YOUR life and if he cares for you enough to make a commitment, that will include accepting (if not loving!) the things that are a part of your life.
It isn't being selfish to decide that your dogs are too important to you to ditch for a guy. You're not choosing an animal over a person really. You are choosing to value your choices and lifestyle more than you do a person who doesn't respect those choices or lifestyle.
My husband of 23 years doesn't like dogs. But he knew when we met that I did and I do and so he has lived with them (more or less happily) all the years we have been together. He is kind and gentle with them and doesn't complain about them. Because he loves ME enough to grow in this area. In return I put up with his various hobbies that most women would b**** incessantly about.