Why does Fury need a sword? He is stronger, faster and much more durable than Skallagrim.
Pretty much just rule of cool, also Fury's physical qualities didn't help him when he was caught in a gushing torrent of plasma last time.
Fury's main weakness is that although his physical body is many times more resilient than any humans (which is only logical considering the weights he can lift) the energy he uses to do this only braces his body, which is useful for when you're being punched but it wouldn't help him if someone swung a sword at him or stabbed him. Hell, even bullets could kill Fury if they wore down his energy shield, which is designed to stop projectiles.
So, without a sword Fury is at a significant disadvantage facing any opponent with a decently sharp melee weapon and the knowledge to use it.
In Fury's timeline he's picked up a world machine as I mentioned, which means he can now utilize his most powerful abilities for enough time to make a real fight of it, but in terms of what energy attacks Fury can use he's massively outdone by Freedom and Skallagrim, who can both manifest street bordering on city level destruction at long range.
Weirdly I've always felt Freedom is probably a stronger character than Skallagrim in a T1 fight, but that's just me.