The speaker is reminded of the expression 猫の手も借りたい , natural mental segue from one cat idiom to another. So just use a functional translation such as "come to think of it...." or "now that I think about it".
The transition assumes shared common knowledge of the idioms in both speaker and listener, so it isn't quite as abrupt as it may appear. If you want to be more direct, "having said that,...."
Not "that a real cat helped" but "a cat really helped". Look at that part again and you'll see it.