Very interesting! My father (1918-1998)always called a tool which he used to pull nails a "cat's paw". It was about 10" long and had a flat end and a curved end, both with a V in the center to hook the nail. Where do you suppose that originated?
An extension of the first given meaning perhaps?

Good day, here it is:

link 1.hammer and cat's paw
The resemblance to a cat's paw is obvious.
I think the whole idea basically comes from this tool; tool first
fable second. (?) metaphor third.(or vice versa)

There's also a cat's paw nebula.
link 2. nebula

You beat me to the "punch."

I have one of these in my toolbox. Good for that occasional oops during framing or for salvaging planks; it tends to rip up the lumber so not used in finish work.

I'd suspected it's name was somehow derived from it's action since resembling that of a playful cat....

This term is also used in the building trades to denote a plaster finish on a wall that is slightly rough, giving it a light "troweled" look.

Helen, could this be the cat's paw knitting stitch?
Stitch