Should the hands be used for absorbing the impact after a jump? I am trying to learn some very small jumps and bunny-hops. It seems that upon landing from either, there are two options. I am talking here only about the moment of the impact with ground, and not about manoeuvring pre-jump or in the air.


Upon landing, one can push with the handlebars down. This seems to have the advantage of delegating the work of absorbing the impact to the forks, which is what they are made for (assume hardtail).
Alternatively, one can strive to stay centered on the bike, relaxing the hands, and absorbing most or all of the impact by the feet. This seems to be achieved by kicking downwards when the bike is just about to land.


IS any of those techniques the correct approach? Or am I completely off?
Your assumptions are wrong. Yes, riders do extend their hands and feet just before landing, but not to make the bike work more. They do that so they can make room for the inevitable hand and feet compression which will happen when contacting the ground. If you don't extend hands and feet then you only have:


40cm absorbtion of hands and feet compression
15cm absorbtion of fork and rear shock (on a 150mm travel bike)
2cm absorbtion of tyre compression


anything else is pain on the body and bike.

If you do extend the hands and feet just before touching the ground then you have:


80cm absorbtion of hands and feet compression
15cm absorbtion of fork and rear shock (on a 150mm travel bike)
2cm absorbtion of tyre compression


This video shows an extreme landing at 1000fps but it displays the extend-before-land technique very well: