Let's say I provide the silver cable to a headphone shop. Do you think they can recable it for me? Or is DIY easier
They'll do it, probably for a fee, though it's not difficult to do this at home.
First, order the wire and (if you like) the nylon mesh. I mentioned the company I went to. There are others out there. Shop around. You can order this wire already braided. I went with a four-wire braid because it allowed me to divide the common ground wire into two separate grounds. It may not be a true "balanced" cable, but it does minimize - as much as feasible - the issue of groundwire interference.
One consideration is length. Grado cables are typically 9 or 10 feet long. To me, this is more wire than I need. I rarely sit across a room from an audio source. I use my iPod a lot, so four feet was both cheap and practical. I also wanted a shorter cable to minimize the length of the signal path. I doubt an extra foot or two would have had much impact but why pay for more cable than you need?
Be sure to use at least two colors for your wire. It's possible to have four wires with four separate colors but you want at least two. That way, you can designate two wires as "ground." When you open up your cups, you'll see a common ground wire with the same color: black. Just solder your ground wires, then the other two.
At the connector, you'll want to make sure you solder the two groundwires to the right connector part. The long piece at the bottom is the common ground. Once you have both wires soldered, you can add the wires for the left and right channels. How do you know which is which? It doesn't matter. If you get them mixed up, just unclip the cups from their forks and switch them over. This is a basically stress-free way of getting it right.
There are logistical issues to think about before soldering. The mesh needs to be the right length. I just guided my braid through it, then cut off the excess. I found it easier to draw the braid through from the front than to push it through from the back. To do this, just pull the sleeve back, the way you might roll up the sleeve of your shirt, either exposing or grabbing the front of the braid and pull it forward.
Of equal importance is to make sure you load the right parts in the right order when assembling the connector. Most connectors have a little shuttle that goes into and sticks out of the outer shell. This should be the first thing pulled back from the wire, followed by the outer shell, then the plastic overshoe (to keep the connector parts from shorting out from contact with the metal shell). The front of the connector should obviously be the last item on the line. If you solder in the groundwires first, you can't go wrong in soldering in the left and right channels.