The thing about a cat's paw, at least as far as my Collins dictionary is concerned, is that it doesn't involve a cat.
Despite this, finding a cat is still probably your best chance of spotting a cat's paw. In fact in this case you'll probably find four.
Try looking near the base of the cat.
If the cat in question is a ship's cat then you may just see another cat's paw somewhere close, because this is a knot used for attaching a line to a hook.
If, on the other hand, you wanted to take the hook off the place where it's nailed up, then you might pull the nail out with a cat's paw nail-extractor. But probably not, because they do gouge up the timber quite a bit.
If the wind is light then you may see cat's paw all around your ship, because in this sense cat's paw is the pattern of ripples on the surface of the water where the wind has ruffled it so that it looks a bit like paw prints.
Not only that, but there's just a chance, if your ship's near a river, that your rations might include the cat's paw mussel.
Lastly, that stupid hulk of a ship's mate? The one the captain secretly encourages to keep the crew brutally in line so that the captain can himself remain remote, dignified, and even popular?
The poor sap's a dupe. A cat's paw.
So, answer me this: what does that make the captain?
Spot the frippet: cat's paw. The word in the last sense comes from a Fontaine story about a monkey who uses a cat's paw to draw chestnuts out of a fire.
So the captain in the scenario above is actually a monkey.