First, you need to export face gen data for each NPC. You can do this by selecting the entry for the NPC in the Creation Kit, and pressing Ctrl + F4. If you have multiple NPCs, you can hold down Ctrl and left click each entry so all of them can be selected. While they're highlighted, press Ctrl + F4.
You can find this under Skyrim\Data\textures\actors\Character\FaceGenData\FaceTint\ModName.esp and
Or, under Skyrim\Data\textures\actors\Character\FaceGenData\FaceTint\MyMod.esm and Skyrim\Data\textures\actors\Character\FaceGenData\FaceGeom\MyMod.esm.
For example, let's say I exported face gen data while Urklawad.esp was open. I would find the face gen data under:
You would package these files with your mod just like any other. As long as you package all files in both of these folders, you and your users should have no trouble with the gray face bug anymore.