The most interesting 'dragon' which is not dragon-type, according to Dragon Tamers...
The dragon tamers at the Battle Frontiers in Emerald and Platinum both have tables of Pokemon they can use, and all of them check out as 'dragon adjacent' Pokemon. Lance's Pokemon, Tyranitar, Nidoking, Feraligatr, Milotic, Bastiodon, Kangaskhan and Arcanine (Lance used the last 2 in Stadium in the 90s, only Electabuzz didn't make the cut). Most all of them are either dragon-shaped, in dragon egg groups, or has previously been used by Lance within the franchise to establish their place as a 'dragon' despite lacking the most common association, type.
But the weirdest of the list, by far......... is Skarmory. So, Skarmory may be a dragon?
Linked above is the stat info on Skarmory within the Battle Frontier's Emerald and Platinum tables for the Dragon Tamer trainer class.
Considering the first location we ever see the Pokemon in is just outside of Blackthorn, perhaps the natives have a more intimate knowledge about the Pokemon that shape their view of it as a dragon. I mean, they don't see Ursaring as a dragon and it's also somewhat unique to Route 45. So it's can't be just the proximity, there's something about Skarmory in particular.
The Shield dex entry for Skarmory mentions Skarmory is "used for heraldic designs" but we don't see that yet anywhere in the franchise. However, I did find one of the Pokelids in Tokorozawa, Japan:
Considering Skarmory's association to weaponry, and the common idea of 'slaying dragons', it could be seen oppositionally to dragons in a way that also includes them. Perhaps 'we're not so different, you and I'. In Pokemon Emerald, the dex entry reads: "People in the past used feathers fallen from Skarmory to make swords and knives." Sun, the dex entry reads, "In times long past, warriors used [Skarmory feathers] as swords." Something about the history of Skarmory's feathers seems to have remained an important aspect of the Pokemon's status to the Blackthorn people. Their notion of what constitutes a 'legend' is often freely equated with dragons.
"You likely know that dragons are Pokémon spoken of in legends!"
Lance, Pokemon Let's Go Pikachu & Eevee
So in conclusion, I do believe Skarmory is like the "Johto" version of Arcanine, a Pokemon natively spoken of in legends and respected by Blackthorn's Dragon Tamers as a legendary long after the rest of the world changes their perspective of these Pokemon.