Back when I could still sleep on a Thermarest, I deflated it, folded it in thirds, let a tiny bit of air back in and put it in the pad pocket in the back of my pack (needed there since my pack itself has no padding). I still do this with my insulated air pads. (No need to put air back in if the back of your pack is padded.) You could do the same with a hydration bladder pocket. No stuff sack needed and the pad is fully protected.

I agree with the others that any inflatable pad belongs inside the pack for safety. I like W_D's idea of putting it inside the sleeping bag. A fully deflated Thermarest (I found that you really have to roll it up twice to get all the air out) shouldn't take up that much space.

I also agree that if you don't have room for everything inside your pack and its outside pockets, either your gear is too bulky or your pack is too small. First, read the articles on the home page of this site, left-hand column to see if you can eliminate a few items. If that doesn't work, then maybe a bigger pack? While I can go out for 10 days with a 43-liter pack, not everyone can get their gear that compact!