My suggestion is the same as Epric002–a foster to adopt arrangement. Or, work with an organization that has fosters for its dogs (e.g., City Dogs Rescue, Lucky Dog, Lost Dog, Washington Humane Society, etc.) because they can tell you a lot about a dog in a home setting vs. a shelter.
You can also express interest in a dog who has been living with and is good with cats, although that’s no guarantee your cat will like being around a dog.
Good luck! Hope to see your adopted dog on a future Animal Fix.