Kote-men

For a while now I have been trying to understand nidan waza and I think that the answer is kote men.
The first cut is the kote cut. I think it is easy to believe that the kote cut has the same value as the men cut, but if you think about it if you were to chop off your opponents hand this would not really be of any use to you.
I believe that the kote is a shock cut. It is performed lightly and sharply to shock the opponent into making a strong move against you.
The next is a standard men cut which has to be from the top of the head.

When I was in Japan one of my sensei got very annoyed because my kote cut was much too big. The foot work was the same as a men cut and kote also the same.
He said cut like this and stamped his foot almost without taking a step forwards at all.
Another sensei used the sword as if he was taping in a nail like another good sensei said to do because my wrist was much too stiff to perform the full movement that the shinai has to go in.

My problem now is I can't perform kote men in one movement. I have been thinking of shime and a video I saw of Ueshiba sensei who invented Aikido. He warmed up by performing a kind of dance, stretching out his too fists then pulling them back.
I believe that this is the kind of rythm for nidan waza.

• The hands should not extend when performing kote. They should extend then move in a circle back to there start position.
  
• The kote cut should only be in the wrist, as in hitting a nail with a hammer.
• The kote men cut should be fluid and use no power in the kote cut.