Only in TSL. There's no provision for a texture override in K1's heads.2da, so you have to edit the model.
The OdysseyBase/AuroraBase name must match the filename. MDLEdit will only allow you to change the textures in a binary model. To change the name of the OdysseyBase (or anything else), you'll need to either decompile the model, edit the ASCII and recompile, or hex edit the binary model. It always used to be wiser to do the latter, since ye olde MDLOps would typically break a lot of models in the decompiling/recompiling process, but that's not as much of an issue with MDLEdit and new MDLOps. MDLEdit does still have some bone index issues though, messing up skin weights in some cases, so that's something to keep an eye out for.