Just figured this out...

[Kalliope]

On my rogue, I unequipped her main hand dagger and transmogged her offhand to that appearance. I then reequipped the main hand dagger for a matched set with no problems. I assume that this only works if the weapon can be equipped in either hand to begin with, but it's something to keep in mind!

[Teigan]

That could be useful. Thanks for pointing that out!

[Kurasu]

Oh hey! I don't know why I didn't think of that! Thanks for the idea. I'll definitely keep that in mind.

[Sigrah]

I had a similar issue with my shammy. I thought I would need 2 copies of the same axe (one for each slot) in order to transmog them onto my other axes. Turns out I could use 1 copy of that axe for both the main slot and off hand slot at the same time. When I realized this, I felt extremely stupid and was like "why did I spend 2 weeks getting a second one when I had the first one after the second day?"

[Kalliope]

At least you weren't lazy! That was the whole reason I ended up trying it!