It's definitely possible to strip teflon insulation by hand. I did it for years before finding the hot-tweezers in a surplus store. The secret is do not try to use a pair of strippers! Unless the size match is absolutely perfect, you will either break the wire or nick so many strands that the connection will be mechanically weak.
The razor blade or x-acto knife approach is far safer. Use a light swiping motion, holding the blade at 90-degrees to the wire. Even with thin wire you can feel when the blade gets through the insulation. After you make a couple of nicks, it should pull off using a thumbnail. Take a close look through a magnifier to check for broken strands. A few is fine, but if it's more than about 25% shredded cut it off and try again.
If you are going to do a lot of termination on teflon, the hot-tweezers are majorly cool. Once you get the temperature dialed in (5-900 degrees, depending on insulation characteristics), it's just a matter of a light pinch, twist and pull. Fast, and no broken strands at all. I do a fair amount of work on classic computer systems and often need to use 30g Kynar wirewrap wire for repairs or modifications. Wirewrap wire is solid core and breaks even easier than the stranded cable. The tweezer system was the best $25 I even spent.
If I go the Graph-Tech route, I'm probably going to take a deep breath and try tacking on new pins under a magnifying glass. Butt splicing and heat shrink is fine, though. I'm just fussy...
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