Most people carry their DL in their wallet. I don't recommend evac'ing without your wallet.

In my state the DMV takes your thumbprint and that (plus your pic) should be enough to re-establish identity if you lose your DL. I dunno if all states do this.

Other docs, I'd say scan them into a computer and put a CD-ROM copy in your safe deposit box. If you really want to have a copy on your person, use a USB thumb drive (some of these are very thin and can fit in your wallet's coin pouch--you can even use a mini-SD card which is fingernail sized). Encrypt the files if you're paranoid.

Renew your passport soon. They're going to start putting RFID in them, which can be read from a distance, and their "privacy" fix will be to advise wrapping the passport in foil (there will be foil lined passport pouches). Foil will stop the RFID from broadcasting your passport number to identity thieves, but of course it will be visible on metal detectors. So if you have your passport, cash, and other important papers in a "hidden" neck pouch and then get wanded or go through a detector arch at an evac shelter, ding ding ding, your "privacy enhancing" foil wrapper has just revealed where your neck pouch is. It's better to renew now and get a passport with no RFID before the damn morons put RFID in all of them.