Got anything concrete you think about the game? You're gonna not be thinking anything is concrete with an attitude like that.
The Goryshche fate alludes to the idea that like the Chimera, the Hydra is an Allagan creation. The fusion of multiple dragon heads onto a single dragon body. Since the Goryshche is still a Hydra in pain after 5,000 years, it's likely that the Allagans also inhibited the dragon's innate ability to change forms.
You've either missed or ignored what this FATE implies. It's as close as we're going to get to the game spelling it out for us. All Hydras exist due to Allagan experimentation. Like how all Ixali, Chimeras, Lamias, Ananta, and all the other stuff that the game tied into this plot point do. This means, unless otherwise stated, that all Hydras are dragons by their ancestry.
As for whether or not the Five-Headed Dragon is a voidsent wearing dragonskin or not is irrelevant to the topic at hand. The topic at hand is that, is there a way for dragons to get to other shards in any way, shape, or form so that legends and myths could be made about them? The answer is yes.
Consider this. Where is the Five-Headed Dragon? It's on what's left of the 13th. If it's a voidsent, why is it in the shape of a Hydra, adhering to fighting as a Hydra instead of in its true voidsent form? Ultimately it doesn't matter, and we could endlessly speculate or theorize as to the whys of it. Fact is, it's in the shape of a dragon. For whatever reasons it takes that shape or that body, it knows about dragons. It knows what dragons think. It knows their language(Think of Voidsent possession and Ascian possession of living hosts). And it's been there for thousands of years.
Also there is the trash monster, the Two-Headed Dragon. Which maybe a voidsent in dragon form. This is even better for our purposes of hashing this out, because the other place Two-Headed Dragons show up at is in Newvoid in Eureka Anemos. Whatever is in Eureka that allows voidsent to cross the veil so easily is unexplained, but they do with a frightening frequency, given that there are no summoners(in the creates portals sense) to create blood pacts or open void rifts.
It follows that all we need for voidsent to show up on other shards is areas like Eureka, traditional sorcerers that surreptitiously perform void portal rituals, or super civilizations(Ronka/Allag analogues) that create stable true portals. Anyone of the three will suffice, and all that need happen is that a voidsent with a penchant to take dragon form cross over.
This is my actual logic train.
Goryshche is a hydra by appearance. (Undeniable)
Goryshche is a dragon by fate text implication. (You could also read the FATE to just be saying that he was a poor likkle Hydra that got some nasty unperceivable experiments done on him, but that would be a worthless read)
By other plot threads from both fates and dungeons and sidequests, Hydras have been implied to be experimental dragons created and distributed by the Allagans like many other species.
Five-Headed Dragon is a Hydra by appearance and a dragon by name and implication and exists in the Void.
Two-Headed Dragon is a Hydra by appearance and a dragon by name and implication and exists in the Void as well.
Therefore the Void took or was given dragons at an undefined point in the past.
The Void is accessible by sorcerers and technology on every shard.
Therefore it is highly probable that dragons were brought to the other shards by the Void.