A Wyvern is generally a two-legged dragon that stands upright and slouched (like a Tyranasaurus). In most mythology Wyverns are also most of the time very small dragons. Often seen owned as a pet that an owner walks around with, having it perched on their shoulder like a Pirate does with a Parrot.
A Wyvern IS indeed a type of dragon. Not a serpent of any kind. Nor any other type of reptile.
A Wyvern CAN be made up in any lore as part Wyvern, part serpent, part what-the-hell-ever. And be called a Wyvern still in that specific lore.
Just as vampires and werewolves are made slightly different per person's lore creation. Wyverns can be made different too. But neither original lore is ever actually changed. It is simply altered in some one's specific story.
Such as with the Twilight Vampire series... Vampires do not sparkle. Nor are able to walk in sun light. But in this specific lore they do and can. Taken the original lore and creating ones own off of it.
That being said... even in dragon form Shyvana is not a Wyvern of any kind. She is insanely large(even though there is nothing saying a Wyvern can't be large). And she walks on all four legs. She is the definition of a literal dragon being when she transforms.
By comical lore though... in "human form", while she is still half dragon and walks on 2 legs, one COULD say she is a Wyvern for that. But the comical sense being, "Half-Wyvern". But only in a sense of being humorous. That doesn't really exist in mythology rule. And since Shyvana does not transform into a 2-legged walking dragon she couldn't be considered a half-wyvern in her human form. Therefor over-ruling any thoughts that she could be Wyvern-related.
All the above aside... Why was this topic made?
If people troll you then just ignore/mute them. There are a ton of literally brain dead people in this community.