Originally Posted by nathancarter
It would need some sort of reinforcing core - maybe a "skeleton" of thin MDF that's built up into shape with a layer of foam on each side?
Yes, that's the general idea and is covered in many of the tutorials I referred to; however I'd recommend using something other than MDF. Fiberglass or common threaded rods are popular choices, as well as PVC pipe if your sword's blade is thick enough to accommodate it.
MDF can actually be quite brittle as well when used in long, thing sheets and if you were willing to bear the weight of a proper MDF skeleton then you may as well go ahead and make the entire core piece from it for the sake of long term durability.