[OBSOLETE MOD]
It seems to me that CDPR has finally fixed the hair shadow problem correctly, with a properly detailed shadow that corresponds exactly to the haircut worn.
This mod is therefore obsolete and in any case was no longer functional for a long time.
Nevertheless, I'm leaving the files available for those who might find them useful.

As I don't personally use modded cuts, I don't know how compatible they are with the new shadow management.
If they don't work, I don't think I'll be spending any more time looking for a potential solution. I'm a Sunday handyman who doesn't have much knowledge of modding and had fun digging through the game's files out of curiosity, but now I don't have enough time to devote to this activity.

The hair and hats do not appear in the shadow of V, unlike those of the NPCs, we are always bald. However 3D lowpoly models of hair exist, and it is a 3D lowpoly model of the body that is used to render the shadow of V.
So I had the idea to modify the 3D lowpoly file of V's body by adding each of the haircuts. But surprisingly, only half of the haircuts I found have a lowpoly version.

The mod contains a folder ".archive" in which the 158 versions of the modified body are present. So you have to choose only one of these files. And that has for consequence that you will always have the same shadow by session of game, the shadow of the head will not be updated dynamically if you put a hat contrary to the clothes. Personally I never wear one.
Two other folders are present to make your choice. A ".png" where you can see the captures in full definition. And a ".stl" in which you will find the 3D files of the modified body in this format easily readable by 3D software.
Only the female body is shown here but each archive contains the modifications of BOTH bodies!

At the beginning I thought to make only the lowpoly, but I refused to exclude cuts so added the highpoly of the remaining cuts, then I thought of the hat carrier, but it is necessary to know to stop because it was without end. I recovered almost all of the "common" folder (only the cuts only designed for morphs other than ours, and what clearly has no impact on the shadow were not recovered), but I discovered during my research in other folders of other models that I did not recover intended only for NPCs.
The reason why I didn't take only the highpoly of each cut is that these cuts are more frequently subject to bugs when moving, they are not all perfectly attached to the body and can distort especially when crouching, moreover the shadows are blurred enough that the details of the highpoly don't bring anything more unless you are close enough to your shadow and you are in Ray-Traced Shadows (which is not the case on the captures).


Known issues

So, some highpoly are subject to distortions when moving, especially when crouching.
I suppose this is due to the connection with the body not being good enough yet.

Doesn't work in photo mode without ray tracing. With ray tracing it's not my mod but an exact projection.
This indicates that the photo mode uses another model.
I didn't find this other model, and honestly it's even more crap because this shadow isn't even impacted by the clothes. So I don't think I will do anything about it in the future.

Johnny is also affected by the mod when we play him in the basic version. An optional version allows you not to have this problem but it is only for female V players. 
Indeed, in the basic version, the haircut chosen is applied on the lowpoly of the female and male body which applies the hair in question on the shadow of Johnny. In the optional version the haircut is applied only on the female body and Johnny's haircut is applied on the male body.


Installation (Vortex is supported)

Choose ONE archive from the ".archive" folder, and put it in the mod folder at this address in the game folder : ...\Cyberpunk 2077\archive\pc\mod


Uninstallation

Remove the chosen archive from the mod folder.


Credits

A special thanks to the WolvenKit team who finally made me discover the modding world from the inside a month ago thanks to their user friendly software. A fantastic tool. This is my first official mod after some exploration with personal modifications of existing mods.

More

[MODDING TUTORIAL]

Create a Shadow Hair version for modded haircut

Judy has a tutorial for anyone who wants to create the shadow of a modded haircut that is therefore not present in the classic Shadow Hair archive.

If you want to put your files here rather than on a separate page, you can send me your files by private message and I will put them in the optional files.

Thanks to DanRuta for his very impressive xVASynth tool.
Sorry in addition for the translation DeepL. ^^