There are two kinds of wrist action possible in the golf swing. One is wrist-cock. The other is wrist-bend. In a full swing they are usually both present to some degree. But I would like to try to persuade you that in a short swing, suitable for chips around the green, it is wrist-bend that will give you the better service.
Let me first define my terms. Wrist-cock, if you hold the club in front of you, is an up-and-down motion. Wrist-bend is a back-and-forth motion. The left wrist arches and the right wrist bends back.
Personally I'm inclined to think that the advice on chips and pitches "Cock your wrists early" is possibly the origin of the term "poppycock." It is a difficult and dangerous movement in the short term. Try it -- this up-and-down movement -- and see for yourself.
But an early wrist-bend is another matter altogether.
Most golfers use it when they putt, even the ones who will assure you they don't. The greatest putting master of old times, the South African Bobby Locke, used to say he had no wrist movement at all. Movies prove him mistaken. He had a slight, but definite, wrist-bend.
On pitches and chips you will find this kind of wrist action is also extremely valuable.
Try arching the left wrist early on the backswing. The right hand will automatically bend back. Now swing through with the feeling that the left wrist is still firmly arched as the clubhead "goes through the ball." Or, if you prefer, feel that the right hand remains bent back all the way through the shot.
The day I concentrated on this technique more than on anything else, I had seven single putts and four "gimme's." I recommend it to you.
I might add that it can also be a useful technique in bunkers. But, of course, practice first before you use it.