Is there any official reference inside a 5e book that makes specific note of any dragon (or dragonborn) shedding or molting their scales naturally?
The Dragon Scale mail is the closest thing I can find in official 5e material, which uses the term "cast-off" which is very vague and not definitive, as it could just mean they fell off due to action taken on the dragon's part or were purposefully torn off by them.
Best Answer
Yes
Aside from the Dragon Scale armor that you mentioned, there's the "Who Created It?" table in the section about rolling random details for magic items (DMG p.142), which says, in part:
(emphasis mine)