I mostly see nirnhoned on Stamina weapons. So bow for ranged fights, axe if going Dual Wield or One-Handed or greataxe for Twohanded, for the bleeding passive you get from axes. Axe is often paired with a dagger for DW, but you get limited benefit from the off-hand weapon trait so its not always worth the cost of putting nirnhoned on your off-hand.
If you want it on a staff, Inferno staff is for single target damage and Lightning is for AOE.
Or you can do it like me and research nirnhoned on mauls first, which I never use but I accidently accepted a Master Writ for before I'd learned the trait.
Here's another angle. I've made about 50 million gold by buying master writs, completing them and selling research scrolls and furniture plans which I bought from the writ vendor. Almost ALL of those master writs were Nirnhoned, and 80% of those were weapons.
Therefore I would research that trait asap if you want to do writs, especially with Woodworking and Blacksmithing weapons.