So I decided to write to Shearwater and asking if he wanted to try and make a C recorder whistle for me.
It was very helpful and after some experiments and prototipe he made a C recorder whistle for me with a good priece.
It is very good and is working well even if I had to make some minor adjustments: intonation seemed fine but playing known music I realized that could be better.
For this reason I have enlarged a little some holes: the 3 in particular (starting from the bottom).
I have also tried to polish the windows and in particular the labium, that was a little rough and coarse: the sound is significantly improved.
I said it to John Bushby (Shearwater) and he promised to enlarge a little the 3 hole and paying much more attention in future whistles about polisching windows and labium.
If you want to listen the sound these are my new videos on youtube: