Having just read two volumes of old school Howard restored, I can attest to the prevalence of the Greatsword as a martial weapon amongst the Hyborian Kingdoms.
They seem quite common with Aquilonian and Nemedian Knights, Nemedian Adventurers and quite a few heavy infantry mercenary units.
So, I'd say it's a fair cop to consider the greatsword a Hyborian weapon.
As for textual evidence - there's plenty of that in The Hour of the Dragon for example.