Seeing as the Elves have access to 'regular alloying elements' and other interesting elements (someone mentioned Titanium) and that rarity was a non-issue, I'd recommend looking into Titanium Aluminide, it's an alloy of Titanium and Aluminium that's being looked into as a replacement for Nickel Superalloy jet engine blades (one of the most brutal applications possible for a metal). This means it has to be incredibly strong and stiff which is ideal for making swords.
Some other notable alloys are Nickel Aluminide, a curious compound that not only is really strong (also used in making jet engine parts) but has a rather unique property that it actually gets stronger as you heat it (at least until ~800°C where it starts behaving like normal metals again). It's because of this that it's sometimes used for making rollers for the steel industry for hot working red hot steel.
Stellite is another candidate, an alloy primarily of Cobalt and Chromium with a bit of tungsten and carbon thrown in (typically has 1% Iron, but you could probably leave the Iron out altogether without much trouble). Stellite is primarily used for making cutting tools (saws for cutting steel) and valve parts for car engines.
You may even be able to use Tungsten Carbide tips for things like arrows (Tungsten Carbide is used for making rock drills). It's very dense but extremely hard, I pretty much use carbide bits for all my metalworking because carbide bits shred through steel like butter (imagine arrow heads that can easily puncture everything including quality Iron armor...)
You could even use Silicon Carbide tips/edging, seeing as both are some of the most abundant elements in the world, it could be a very cheap way to add a much needed edge to an otherwise inferior blade. SiC is used for making steel cut-off disks for angle grinders. Not to mention it has a really bad-ass black-glass appearance.
Just because you can't use Iron doesn't put you at a disadvantage at all provided you've got some advanced metallurgical know-how. If anything, some of the strongest alloys and ceramics (technically Carbides are ceramics) either use relatively little Iron or don't use it at all.
Addendum: If you want to get really 'out there' with regards to your material selection, check out depleted Uranium. Because, according to everyone's favorite encyclopedia: "Depleted uranium is favored for the penetrator because it is self-sharpening and flammable. On impact with a hard target, such as an armored vehicle, the nose of the rod fractures in such a way that it remains sharp." The catch? It's flammable, poisonous and mildly radioactive... which I suppose is fine if it's going to end up embedded in someone you don't like anyway.