Well, what I do know is that
wyrm also can mean "serpent".
What I did find through Wikipedia is this 17th century Icelandic picture of
Níðhöggr (Nidhogg) gnawing at the roots of
Yggdrasill:
Looking at this, I'd say it looks pretty serpent-like.
Also, since Tolkien was inspired by Norse and Germanic mythology, I assume that he definitely uses their descriptions of dragons as inspiration and was familiar with the Northern European style of dragon.
As for modern adaptations of Norse dragons, I rather like the look of dragon in Sword of Xanten (here's a
clip on youtube of it), which is Fafnir (and we know Tolkien liked this story - Also notice that in this movie he uses the term "Worm")
Obviously, this is only one example, and Tolkien tells us that they have four legs, which leads me to think that they are maybe more crocodillian. Because I can't imagine a dragon walking like a lizard, I'd say that their legs would be similar to a crocodile's, where they are only "half-raised", not fully like mammals or dinosaurs, but not all the way down like most lizards. I think that they waould walk a bit like
this, and would look more like
this, when resting, though I imagine to have a larger, rounder underside than crocodiles and more like some early dinosaurs or pre-dinosaur reptiles.
If we're going for realistic examples, perhaps they looked a bit like
Dimetrodon's without the sail, or maybe more like a
Proterogyrinus (the reptile in the picture). Or maybe more therapsid (mammal-like reptiles) such as
Estemmenosuchus or
Bauria. Or perhaps, if they're skinnier like worms, A
Doswellia would be more appropriate. Though I would personally go for a cross between a
Moschops and a Doswellia.
Ok, I've probably bored you all with knowledge of early reptiles, but I was just trying to show examples of creatures from the animal world (however extinct), which I think are similar to the Worms of Middle Earth. Obviously Tolkien did try to make his animals really work, so that's why I was taking the scientific approach here as well.