They're Just Shorter Swings
There are all sorts of theories regarding the way to hit pitch and chip shots. Ken Venturi, a fine teacher, advocates an absolutely stiff-wristed technique. Phil Rodgers, another excellent teacher, professes an extremely wristy method.
Frankly, I think both of them are making things too complicated. To my mind, the pitch and chip are simply small golf swings. Your stance, which narrows from the driver to the short irons, narrows still further for the pitch and chip, and also continues to open up as on the short-iron shots, to the point that on a chip shot your heels are no more than 15 to 20 centimetres apart and you're aligned about 20 degrees left of your target. Your ball position remains the same as for all your shots, somewhere off the left heel to the instep for most people.
From a compact stance, you simply make a proportionately compact swing at the ball. Wrist action is neither restricted nor forced - it's as natural as in a full swing, the result of a swinging back of the arms.