Just to clarify... The wrists are never consciously 'hinged' the only time we ever focus on the 'hinge' is when we are trying to educate or train the hands to work correctly whilst practicing.

Chipping action
Within the family of short game strokes, chipping and putting are very close relatives with only two slight differences.
Firstly, the setup with ball position ALWAYS favouring the back of the stance. Secondly, a more positive, pronounced set of the triangle allowing constant depth control.
As to the swing itself, EVERY golfer should, from time to time, rehearse and practise a descending blow. After a while, there will be no inclination to attempt to help the ball into the air and pure ball striking will be simplicity itself.

Pitching - The mini-swing
The difference between chipping and pitching; second gear! The pitch is inevitably a longer shot with more height required. We therefore need more acceleration and allowing some wrist hinge will do these two things for you with no extra effort.
We are right back to our basic swingbuild exercise, the half swing, rehearsing it, practising it and then trusting it on the course.
By turning a little bit less or more, you learn to judge what is required to play different shots, but, the same swing mechanics apply throughout with the same check points.
Just think of it as a short swing.