After this DB update, the off-hand sword is the absolute worst place to put nirn.
For traits that affect character-wide stats like sharpened, precise, defending, et al. it doesn't matter which hand you have the weapon in. A sharpened trait on the off-hand has the exact same effect as a sharpened trait on the main-hand.
Nirn, however, affects the tooltip stats of that item and is not character-wide.
For dual-wield, you get 100% of the damage from the main weapon, and only 20% of the damage from the off-hand weapon. All that the passive does is lessen the impact of that off-hand penalty. Furthermore, this passive only affects weapon damage, not spell damage, which is why dual-wielding casters never even bother with it.
With the way nirnhoned works in DB, you should never put it on the off-hand weapon. Use a trait that gets full potency in that slot, not a trait that will have to suffer an 80% penalty. Actually, you're better off just running sharpened on both. But if you already have nirnhoned weapons and can't afford to recraft them as sharpened, then you can keep on nirnhoned weapon on the main-hand and replace the off-hand with sharpened.