A Transmog question - does changing professions affect a T-mogged item?

Greetings, Folks!

I haven't found anything specific on this, apart from "what you can't equip can't be transmogged".

In my case, I have tailoring and enchanting on my lock, and have already used transmogrification on my shoulders and belt to lend them the appearance of
- Primal Mooncloth Shoulders in the case of my T10 shoulders;
- Primal Mooncloth Belt in the case of my Crushing Coldwraith Belt.

Both of these clothes require tailoring to wear themselves. As a PvE character, I was happy with tailoring, but for whatever reason, I would like to be more efficient at defending myself in wPvP / BG's, and am planning on dropping tailoring for engineering.

What will happen to the two 277 Ilevel items on me?
- Would their appearance be reverted to their original look?
- Would they maintain their Primal Mooncloth looks, but will become unequippable?
- Or will the profession reroll have no effect on them whatsoever, and I'm free to keep the profession-linked item looks despite not having tailoring anymore? If this latter is the case, what would happen if I unequip and re-equip the T10 shoulders and belt? Nothing?

Thank you in advance for any crumbs of knowledge! :)