*Disclaimer - I don't sell Piccolino cables - this is just for fun*
Finally found the right way to prepare Piccolino without an expensive automatic stripping machine. The key to any problem like this when you have a new wire and want to find a way to strip it perfectly, is to go to the Home Depot and buy every wire stripper they have and try them all with each setting.
Background. Piccolino is a very expensive Dutch coaxial wire with what appears to be silicone-like jacketing, a silver plated copper outer shield (typically used as a negative conductor), a thin teflon tape insulating layer, and a well-armored, tiny internal core with heat-proof abrasion-proof Kapton surrounding six tiny ~0.12mm strands of silver-gold alloy wire of a proprietary mixture, protected with kevlar stranding around them. The difficulty level of removing the Kapton layer as well as the rarity of this wire means that few people DIY with Piccolino. If you ever are in a situation where you need to strip this wire, here is how.
Step 1: Buy the Klein Tools 11057 stripper
Step 2: Remove the outer jacket (use the 22awg hole or a larger Klein Tools stripper - this part requires very little finesse as the outer jacket is fairly thick) or cut away the entire outer jacket + outer shield if you only want to use the center conductor (use the 24awg hole on the 11057).
Step 3: Use the 30awg hole to strip the teflon and Kapton from the center core. In repeated iterations there was no damage or nicks under magnification of the internal silver-gold strands. Normally you need a custom die machine to strip such a thinly-insulated wire, but in this case, the Klein is just a perfect fit.
Step 4: Gently move the strands to one side to isolate them from the bundle of kevlar fibers that they are surrounded with, gather the kevlar fibers and cut them off with flush cutters.
Step 5: Success