When wiring up projects at TechShop, I find myself using wires that are much to small for my wire stripping tool. Through trial and error and many damaged wires, I think I've come up with a great method for removing the shielding without damaging those delicate metal strands inside.
Step 1: Nick the Shielding
Some shielding will yield in the next step without having to cut all the way to the core, which is better for the conductive wires, but some stubborn shielding won't give unless you cut all the way through in at least one spot. Whenever possible, I try to stop before I break all the way through the shielding to avoid nicking the wires inside.
After nicking the shield, if you bend the wire away from the nick you can get a better idea of how much of the shielding you've cut, and it opens up a bigger gap for you to grab in the next step.
Normally two nicks in the shielding on opposite sides of the wire is sufficient.
Step 2: Grip the Notches in the Shielding
Having short nails helps a lot here as you can really get some good leverage when you start to pull. Longer nails tend to bend, and if they bend at the nail bed, it's not a pain-free experience. Short nails, people.
Step 3: Pull the Shielding Off
If the shielding is properly nicked, it will tear neatly between the two nicks and pop off the end of the wire without much trouble. If you are unable to pull the shielding off, go back to step 1 and either deepen existing nicks that have not yet made it to the metal core, or add additional nicks around the shielding.