Michael Hirst’s VIKINGS depicted an execution by decapitation in the first episode. It is interesting to note that Jarl asked the convicted man for his preferred manner of execution. The condemed chose punishment by decapitation.
A convicted Viking would most likely request to be executed by the most honored named sword in the warrior community. If death was not rendered by sword, then death was to be by arrow. These two execution forms assured the Viking of his all-important entry into Valhalla. There he would join Odin’s celestial Army for the battle at Ragnarok, the end-times war, against the Giants.
A true Viking of that time would never select decapitation and the reasons are found in my Amazon e-book, “To Kindle A Fire,” © 1999, by Richard Yarus.