Why not just try it yourself and see how much damage you lose. Nothing like an internet forum will ever compare to the raw experience. Find a chonky overland mob or go find a parse dummy and see what happens to your numbers.
From my answer you could deduce it is less damage, but since you didn't I'll just say it's less damage. You're essentially making your nirnhoned weapon less effective and putting a lower wep damage in the main hand, instead of your high damage item in your main hand with a small buff from the lower damage item.
Here's math: Nirn gives 15% damage. Passive gives 6% damage. Main hand nirn gives 15% + whatever off hand's calculation if. If you swap, off hand nirn gives 6.9% wep damage instead of 6, and your main hand gives 0% bonus. So it's a total of a 21% bonus vs a 6.9% bonus.