Strange, link works for me even from incognito mode. Does your browser not like dropbox maybe? I'm not sure what part to clarify though. If the term "splice" is the part that's throwing you off, that means I did this:
Nif1: NiTriShapeData -> Copy branch
Nif2: Paste at end -> Go into corresponding NiTriShape and edit node to point at the new ones instead of old -> Delete old node
Then repeat for BSDismemberSkinInstance.
If you're wondering what's different between the old nodes and the new ones, this sentence here was meant to clarify: "The mesh is literally a vanilla dragon mesh with minor edits to some vertex locations to alter the shape of the dragon" but without you seeing the mesh there's really no way for me to explain that in more detail. The biggest difference is that it now has more spikes.
The splicing technique generally works; see my http://www.nexusmods.com/skyrimspecialedition/mods/695/? This is ~20th dragon I've done this to and this is the first time I've ever encountered this problem, so I really have no idea what might be the cause.