This is a useful article for you, then:
kb.php?a=187The following image was made by Tolkien himself, so should be quite close to how he imagined his (wingless) dragons.
From the picture, I would estimate the dragon's length to be some 20 meters (if the warrior is somewhat less than 2 meters).
Scatha is called the Worm, so he didn't have wings. He very likely did have legs, however (Glaurung, for instance, was also called Gold-Worm of Angband but did have 4 legs). So, 4 legs and no wings would be the way to go.
Sounds like an awesome project by the way! I'm looking forward to seeing this progress.