I am trying unsuccessfully to turn a whistle in wood. I have made several versions with varying degrees of disaster! The main problem I face is the fipple. Just can’t get a decent note. Does anyone out there know if there is a formula/ratio for the hole size, windway, angle and shape of the blade etc etc etc.
I have even tried an existing metal fipple on a wooden shaft and even this doesn’ work. How do the likes of Beezley and Adler do it!!? 
Why don’t you go to the next music store and check out a cheap recorder, like Yamaha’s or Aulos ? You can also buy them used and quite cheap on eBay.
If possible see an Alto model.
They are quite carefully molded, and exact reproductions in plastic of the “real” wooden instruments.
The whistles you quoted are very similar in their head designs.
These are indeed terrific recorders, but the proportions of the head design are not quite the same as in a whistle. This may be due to the fact that Baroque recorders have a conical bore, while most whistles are cylindrical. Lots of other factors too.
FWIW-- My windways and windows are 5/16 wide, and the distance from fipple to blade is 5/32. This is for a D whistle with a 1/2" bore. These measurements are not any big secret, as anyone could easily measure them directly from a finished whistle. Good luck!