Step 2: 'Cutting' through the inner coating
To make this easier, I don't cut the coating, but melt it with the soldering iron!
Run the soldering iron around the inner coating where you want it cut it off. The soldering iron will quickly 'cut' through the coating and will be done in under a second. This does not appear to do any damage to the wires or phosphorous core and if far easier than using wire cutters.
Gently pull off the end of the coating and you should be left with something like I have in the third picture.
Remember, each time you do this, clean the soldering iron on a tip cleaner to get any plastic off the tip!