Not a song, as far as I know, but derived from Egyptian folklore; a "Pocket Tale" as rendered by Peter Kohler

First friend is sitting and whiling away the time. Second friend walks by carrying a cat.

First friend calls out, lazily: "Where are you going?"
Second friend answers, lazily: "To the river. To wash the cat."
First friend observes: "It is very cold today. The cat will die."
Second friend replies: "The cat will not die."

A little later Second friend returns, without the cat.
First friend asks: "Where's the cat?"
Second friend mopes: "It's dead."
First friend can't help it: "I told you that would happen. It is very cold today."
Second friend, miserably: "It wasn't the cold."
First friend: "Then what was it?"
With much distress, Second friend holds up his fists and demonstrates: "It happened when I was wringing it dry!"