But it started as one word, it wasn’t made into one word later afaik. The words also aren’t interchangeable. The thing being talked about is fundamentally nip, not a cat. In a saying like tick tock, the tick part and tock part are interchangeable. In “big bad” they’re both referring to the wolf so again they’re interchangeable. In this case the “nip” part is the same as the wolf part in “big bad wolf”.
If I were to say wolf nip, you’d think of a version of catnip for wolves. If I were to say nip wolf, you’d think of of a wolf that bites people.