You certainly need to make the complete instrument before you try to scale it, as another answer said. Unless the design is an accurate copy of the Yamaha recorder, the pitch of the head joint on its own could be anything. In particular, it will depend on the design of the joint between the head and the rest of the instrument.
To scale an instrument "properly" is a very complicated task. For example to make an instrument that plays accurately in tune, the position of the finger holes depends on their diameter, and professional instrument makers tweak such things by applying single coats of varnish to change the shape of the hole, not by changing the shape to the precision of a 3D printer!
Note that in the pictures of the printed recorder, the finger holes are not all the same size. That is not an accident - they need to be different sizes to make the instrument play in tune. But whether you can print the different sizes accurately enough is another question.
So there is little point worrying about such details, and you might as well scale everything by the same amount. To lower the pitch by one semitone, increase the size by a factor of 1.059. The finger holes should be repositioned in the same proportion.
If you want to be slightly more ambitious, you could apply the same scaling rule that is used to make organ pipes have the same timbre over a wide range of pitches. To achieve that, the high pitched pipes have to be relatively fatter than the low pitched ones. A typical scale factor would increase the diameter (both internal and external) by 1.044 per semitone, compared with 1.059 for the length.
This sounds like a fun project, but you are never going to produce a professional-quality instrument this way, so don't set your standards unrealistically high!
If you wanted to scale the design by a larger amount, for example to make an alto or tenor recorder instead of a soprano, then simple scaling is not feasible. If nothing else, you will need to move the finger holes so the player can reach them, and adjust the intonation by changing their diameter as mentioned earlier. There is no real alterative to either practical trial and error, or very sophisticated computer modelling - and the modelling usually only gives a starting point for trial and error, in any case!