If you actually want swords, I wouldn’t automatically ditch them just yet. Depending on your setting you could use alternate materials.
I’m going to blame all of the Elder Scrolls Online ads floating around for this tangent, but the setting has some interesting alternative materials, or at least did back with Morrowind.
The carapaces from the region’s large insects were re-purposed into a kind of light armor plate, and weapons. My recollection was that the stuff was fragile, but, it’s an idea.
Bonemold was a kind of fantasy plastic, specifically, a resin. They’d mix finely powdered bone with some local glue and the result would be a very hard and somewhat light substance. In the real world I’d wonder about the feasibility of the glues, (waterproof glues are a fairly modern thing), and I’d wonder about it being able to hold an edge. It’s worth noting, if you wanted to go that route, you could use something else as the powdered additive, for some reason all that’s coming to mind is powdered granite.
Stahlrim was described as “unmelting mystical ice.” This was incredibly hard, and would be carved by trained “smiths”, into the desired armor and weapons. It had a sort of roughly whittled appearance, along with a deep translucent blue color.
Ebony is an Elder Scrolls setting standard. It’s actually just mystically strengthened obsidian, that’s then worked and polished to a mirror sheen. In the real world obsidian can be formed into ridiculously sharp blades. So, if your setting has the means to harden it to the level of steel, or tougher, obsidian blades and armor might be viable. Real obsidian has a slightly purplish, or grey translucent, color when it gets thin enough.
EDIT: Since I missed saying this, somehow. In the real world, obsidian is just volcanic glass, and quite brittle. Sharp, but it will splinter apart with no warning, and to the best of my knowledge, it’s not something that can be tempered.
Where I’m going with these two is fairly simple, depending on your setting, you might not need to forge your weapons from conventional metals, you could use any appropriate mineral source from your setting. Stone swords were never a thing, but stone axes and spearheads do have a real world history.
Beyond that, some kind of fantasy wood might be able to hold an edge, and make functional armor. This could get a little strange, but a lightweight hardwood, that’s been properly lacquered, and treated could work as some kind of armor. In the real world, wooden armor was never an effective choice, and wooden weapons were always either for training, or blunt implements (like staves), but, that doesn’t mean your setting couldn’t have “ironwood” or the like.
If you actually want to get away from a sword, I’d seriously consider the axe. It has some nice symbolic qualities, as both a weapon and a tool, and therefore an excellent badge of office to show how the king/suzerain/whatever is in touch with the people. Or to indicate how brutal the world you’re presenting is.
D&D’s Dragonlance setting comes to mind as well, as I recall, the name comes from literal lances used to fight dragons (and, used while mounted on the backs of them.) It’s a major symbol in the setting because it’s function is so important, to the point that it eclipses the sword, somewhat.
Staffs are another possible weapon choice, and there’s some actual history for these as well, with some organizations actually using a staff to indicate authority. It doesn’t have the immediate flare of a sword, and you’d see more of a distinction between a staff designed for combat, and an ornate one as a badge of office.
The short answer at the end is, be creative. It’s what you’re wanting to do in the first place, and stuff like this is only problematic if you want to keep it as bland and gritty as possible. People will use the tools they have access to.