'Wyvern' and 'Dragon' is a distinction from heraldry. Much like stuff like the Griffon not having an eagle's talons, but the Opinicus having those talons and therefore being distinct. But, even then, its a UK distinction, not a worldwide one. In other places the four-legged dragon is a Lindwurm. Tamriel dragons have four limbs, that's just how it be.
(buuuut, someone's already attempted to make one, have fun. https://www.nexusmods.com/skyrimspecialedition/mods/29791 )