A cat's paw is a person who is used or manipulated by another.

It comes from an old fable in which a monkey was cooking chestnuts in the fireplace. When it was time to remove the chestnuts from the coals, he found that the fire was too hot, and he couldn't pull them out. He looked around for something to help him pull them out, but didn't see anything -- until his eye fell on the cat sleeping by the fire. He grabbed the cat, and held it tight while it struggled, using it's paw to remove the chestnuts from the fire.
--Origins unknown

A cat's-paw is a light breeze that ripples the surface of the water.

Cat's"-paw` (?), n.

1. Naut. (a)

A light transitory air which ruffles the surface of the water during a calm, or the ripples made by such a puff of air.

A particular hitch or turn in the bight of a rope, into which a tackle may be hooked.

2.

A dupe; a tool; one who, or that which, is used by another as an instrument to a accomplish his purposes.

⇒ In this sense the term refers to the fable of the monkey using the cat's paw to draw the roasting chestnuts out of the fire.

© Webster 1913.