To my understanding you are completely correct LiR in that a wyvern is a two-legged dragon ... in contast to the four-legged 'welsh' dragon. But both creatures are still in fact "royal beasts": the dragon proper, with four legs, is of course an ancient symbol of Wales and the Tudors' ancestry ... while the two-legged wyvern probably derives from equally early 'celtic' origins. A two-legged dragon is certainly recorded as being used as a Romano-British cavalry standard, and there is even some evidence that is was later adopted as a national symbol by Saxon armies. During the Wars of the Roses the Lancastrians claimed the wyvern as one of their symbols "by right" through Edward the Confessor ... but they were of course probably just manipulating history for their own ends, since the origin and supposed history of heraldic symbols, marks and badges, was then of vital political importance.
None of this, of course, has anything to do with dinosaurs (which is the subject of the thread).