This is actually MUCH easier than it sounds, and demands only the use of NifSkope. For this tutorial we will be making a lightning stag. (You're welcome Vert!)

Step 1: Unpack your mesh using FOMM or a similar utility.
Step 2: Open your mesh in Nifskope
Step 3: Open a New window in nifskope and load up wolffire.nif (can be found in meshes\actor\canine\character assets wolf)
Step 4: select the BsEffectShader block under the main NiTriShape of the fire wold and Copy Branch
Step 5: paste branch the effect shader into your stag's main NiTriShape
Step 6: Replace textures as desired. For a lightning elemental you would replace the GradFireExplosion.dds with GradShockExplosion.dds, and the FXFireScrollTile02.dds with shocktile01.dds.
Step 7: also copy paste in the NiAlphaProperty from the wolf NiTriShape into your own mesh's
Now make the armor addon pointing to your mesh, an armor pointing to the Armor Addon, and a race pointing to the armor.

Good to go.