Generally, there are two common speculations regarding Shadowmourne, and its Alt form.
The first is simple; the "Alt" form is actually the "Incomplete" form. Much like the Sulfuron Hammer before it, it would require some sort of additional quest/item before it actually became Legendary status.
Another speculation I've seen a lot of, is that it would serve similar to an Anathema/Benediction use. Given the nature of Shadowmourne (obviously a Runeblade), quite a few are thinking perhaps it will have a "Tanking" form, suitable to Death Knights, but not exclusively so.
A third theory, however, recently popped up. This third theory is basically, "Anyone can wield Shadowmourne". But, according to his theory, when a Death Knight wields it, it would *look* different. By his figuring, the "Frostmourne-head", the Runes adorning Shadowmourne's blade, all signs pointing to being based on the Death Knight. Even though it's highly unlikely, you have to admit; it kinda makes sense. Again, stats would be identical, it would merely *look* different in the hands of a Runeblade-wielding Death Knight.
Honestly? I'm putting my bet of a Sulfuron Hammer-type of functionality. But I'm *hoping* that perhaps the third theory is right. After all, Runeforging is hardly a substitute for a true Runeblade, which by nature, are Death Knight weapons.