Vikings didn't have bihanders, as these were introduced pretty late, at a time when gunpowder already was invented. Even their predecessors, the one-and-a-halfhanders were classic weapons of late-medieval knights in full plate armor.

They only make sense in that scenario, as you wouldn't need a shield to block incoming attacks. The bihanders themselves were a VERY special scenario as these were used to hack at incoming long lances. Very dangerous, so these guys were payed double the usual fee, hence them being called "Doppelsöldner".

You are trying to create a scenario that was several hundred years in the future of typical Vikings.