The fact that the Plague was spread by rats - actually, by the fleas that lived on the rats - wasn't known until the XIX century. During the time of the Black Death (1346-1353) it was blamed on: bad air, God's judgement, Jews, Gypsies, lepers, beggars, foreigners and pilgrims. Those last two may have been somewhat close to true because travelers may have carried the plague fleas with them.
However, the Black Death was never blamed on witches. The concept of witches as people in league with the devil didn't develop until the around 1428. Other ideas like the Sabbath, flying through the air on broomsticks, etc didn't develop until even later. People were tried for sorcery before that - many of them members of the clergy - but they do not fit with the pure definition of "witch" and the term was never used for them.
As for cats: their associations with witches is mostly the product of modern fiction. The concept of witches having "familiars" - demons or evil spirits serving them, usually in animal form - is exclusively an Anglo-Scottish concept never occurring in Continental trails. Some were cats, but they were also be dogs, rats, birds, ferrets, frogs, toads, rabbits, pigs, horses. etc.
I happen to have three cats and I think only one of them is evil.
