Now that you mention it, maybe I was thinking of Dawnbreaker. I just tried it again in game and didn't get the option to improve that kind of blade, which makes sense. They're still going to require a weapon material keyword though to benefit from the smithing perks, in addition to the improvement recipes.
They keywords are already attached to the items. There just aren't any improvement recipes added yet. I'm going to put together a new way of improving them. Right now I think I will go with using grindstones and weight-stones for improving sharp & blunt weapons respectively. With more exotic grindstones required for the higher level items.
*Looks up Quadrelle* "A small mace with 4 blades"
Huh, I've played a lot of fantasy video games and read more than a few books on historical weapons, but I'd never heard of that term before. Where do you get your information? (Hoping you know about a good website or encyclopedia about historical weapons)
I have a Weapons & Armour Encyclopedia" with pictures.

Written by Matthey Balent. I've had it for years. When choosing names for item I consider historical accuracy as well as ES lore accuracy. Sometimes I'm torn between the two.
Question: if you changed "malachite" to "glass" (a change which I think makes sense, if 'malachite' is what you use to make 'glass' weapons), does that affect any dialogue, spoken or written?
Second question, if it doesn't, can you change moonstone and quicksilver? I get that in Tamriel, "glass" weapons are not literally silicon dioxide, they are some other magic-fantasy ore, and ebony is not a kind of heartwood, it's also a kind of magic fantasy ore. But Malachite and Moonstone are kinds of gemstone, like amethyst or quartz. You can't "smelt" them, you can't turn them into ingots. In fact, they are both known as gemstones primarily because they have stripes, malachite visible stripes, and moonstone a pearlescent appearance caused by tiny planes of crystal. Smelting either of these would just ruin them. Quicksilver is the common name of Mercury, element Hg, the element most known for being liquid at room temperature in its pure state. While I think you can find mercury salts, i.e. it would be reasonable to find mercury "ore," if you managed to refine it somehow you wouldn't get an ingot, you'd get a puddle. A toxic, heavy-metal poisoning inducing puddle. Has anyone seen any explanation for why moonstone, quicksilver, and malachite, all very well know real things with real properties, clearly are different in-game? Is there lore or is it just... I dunno.
As a suggestion, if you do change the names, malachite to glass, I would suggest mithril or something similarly fantasy-ish for moonstone. Maybe make up a name. The same for quicksilver.
As for smithing daedric weapons and armor, I was under the impression that "daedric" items are simply ebony, into which the soul of a very pissed off daedroth has been stuffed. As in, the reason it looks evil is because you crammed someone's soul into a lump of ebony-- and as a daedroth, they are still alive and conscious.
Daedroth are a particular species of daedra. Which do not exist in Skyrim. I do not believe the Daedroth species is a specific requirement. As far as I know it only requires the essence of a Daedra. Which is why it requires a Daedra heart to create Daedric weapons. Like vanilla Daedric weapon crafting. The heart is a sufficient source of essence.
The item name changes do not affect dialogue, and why should they? The people of Skyrim aren't scholars or forum members. They basically just call it as they see it. Just like they incorrectly refer to the Dwemer as Dwarves. I may have corrected the item's names from the player's perspective. But, this doesn't and shouldn't have any affect on the NPC's perception. The same applies to Malachite. We know Malachite is Morrowind's Glass. The Blood of Lorkhan. The inhabitants of Skyrim came up with their own name for it, and that's Malachite. It looks like Malachite to them so they call it malachite. Even though You & I call it Glass and we both know it isn't real-life's Glass that's what it's called. So, No, I'm not going to change what the inhabitants of Skyrim call Glass. If in Skyrim it's known as Malachite, it will remain known as Malachite. Even if the player and his character knows better. There are a lot of things in real life, even to this day, which are named as something incorrectly based on a misconception. Horse Radish immediately comes to mind. It contains no horses.
Moonstone isn't changing. Moonstone is a very ambiguous term and since Moonstone as gemstone doesn't even exist as far as we know in Skyrim it being called Moonstone has no conflict. It actually does look quite a bit like real life's moonstone, at least in my mod, but that doesn't mean it is moonstone. It is a fantasy metal. Why should we borrow Tolkien's fantasy metals instead of inventing our own? Are his somehow more legitimate? Mithril, also known as True-Silver for example simply means that it isn't false silver, correct? Well, if you follow your own logic then Mithril shouldn't protect hobbits or make sharp swords because real life real silver doesn't do either of those things, and yet it uses the same name as silver because it looks like it. How is that any different than Glass, Malachite or Moonstone? It isn't. It looks like Moonstone, therefor it is called Moonstone even if it behaves like Titanium.
Quicksilver has already been renamed Alchemical Silver. Inspired by Morrowind and D&D. Except for the one unique sample of quicksilver included in a quest in Skyrim.