So my best tip for doing anything is take pictures before you start and be methodical, number things go slow and steady, I have made modular cables, shortened cables by both chopping and soldering, and chopping and crimping.
First is getting the tool down the sides of the crimped ATX pin from the opposite end of the wire, without getting them inside the pin, it is tough, be patient and they do pop out with no effort at all, if you're having to heave on them the side parts aren't depressed on the pin. see
here
If you have a crimping tool and parts, simply pop out one wire, cut the wire to length (make sure you factor in the length of the pin / socket in your cut, 2 cm too long is retrievable 2 cm too short is not), strip, crimp a new connector on and reinsert into the ATX connector (listen for the satisfying click that lets you know it has seated properly), repeat (you can use a new ATX connector and just put it in the same orientation as the one you are shortening, chop without popping out the pin, crimp and place in the new one). Guaranteed to get them all in the right place and you get a really quick idea of whether the length was right. Loads of great crimping how-to videos on YouTube my personal favourite is this
guy
If chopping and soldering (no need for the removal tool) it gets a bit messy going one at a time, it means getting all the other wires out of the way and so a helping hands is well recommended, heat shrinking is also a great idea but this is beginning to build in a lot of tools and costs that you might be trying to avoid, insulation tape will do a good job too, just less neat, when deciding where to solder in a wire do think about where the soldering will sit as it will be less flexible than the rest of the wire, see that video above