If someone were to, say, alchemize a working lightsaber, would they be able to use it with their specibus set to bladekind?

That’s a tricky one. A Lightsaber is a sword- But it has no BLADE so to speak. I think a Lightsaber may be closer to Flashlightkind than it is to Bladekind in that regard, actually, buuuut your specibus may reluctantly accede if you try.