Keep trying. If you get a pop up where some dude challenges you on a bridge, choose to fight him. If you win, you get the arcane edge. It popped up for me really early in the game, but I was stupid and threw the arcane edge away or something. Then after I realized what it was for, I think I must've strolled at least 200 times before the popup finally turned up again. This was by FAR the rarest event in the game so far. Even the unicorn popped 3 times and all the pieces of the doomsword turned up before this one dinky little Arcane Edge. Urrrghh.
Note: I'm pretty sure you have to be on the Wizard to get this item. You will not get this interaction with any other hero. So stroll/adventure in the forest as much as you can with the Wizard and hope.
I had a wizard "use map to sail to Effenmont." (As far as I know, this is the only way a wizard can get on a ship.) They came upon a mysterious ship and the wizard chose to search the main cabin, which held an Arcane Edge. (I don't know what happens if you search the hold; this is the only time I've seen this event.)