It might depend on the visual perspective of your game, on whether you intend 3D objects or 2D sprites, and on the specific style that you have in mind.
If you apply the shading when texturing your objects, then it (presumably) won't change as they move or turn--if they do move or turn in your game. Whether that's desirable or undesirable will, I imagine, depend on the things that I mentioned above (and perhaps more).
For example, if you intend to have 3D objects, but that never rotate and that are seen from an isometric, unchanging perspective, then applying your shading in your textures might be easier, and further make it easier to achieve good results.
Conversely, if you intend to have 3D objects that are explored from a first-person perspective, and don't want a static art-style, then applying your shading in your textures may not work--applying them in your code (via a shader, I imagine) might be called for.
(All this presumes that the artist doing this (whether you or someone else) is familiar with the technique in question.)