As much as I like Ulfberht swords, I think they would be visually not distinctive enough.
I have already suggested the second sword from the left here:
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This one:
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It's a too early for the Viking period, instead belonging to the Vendel period, but it would fit the "ancient heirloom" story, which is supported by the saga's but not really be archeology as far as I know.
And it is visually distinctive from "normal" Viking age swords.
But I fully understand Huitie about not wanting to redo renders, and, (correct me if I'm wrong Huitie) this game is not meant to be absolutely historically correct but instead project a certain athmosphere that belongs to the timeframe portrayed but at the same time is light and humourous.
Personally I think of this game as a 3D adult version of Asterix, which I mean as really high praise.
And in Asterix it's also perfectly fine if e.g. Goths are wearing WW1 era pickelhaube helmets, because it's visually distinctive and on-point in the context.