If you know me you know I do a lot of DIY. So, here goes.
For the miniplug on the end, pretty much anything will work, the majority are fine. Silver and gold are both good. Just pick what you like.
Your cable isn't balanced, so perfect geometry isn't a huge issue. Round-braids are cosmetically appealing. I don't like flat quad braids so I don't do them anymore. Or, you can make two twisted-pairs and wind them together into a star quad. I wouldn't recommend using solid-core silver for something like this as it will be stiff and brittle, especially an IEM cable. Stranded OCC copper is probably your best bet, ~24awg. If you want stranded OCC silver you'll have to buy a ready-made cable from Whiplash Audio (as Cryoparts won't let anyone else use it and they're the sole place who has it) which brings me to the next point.
You aren't going to get a hold of those IEM connectors easily. I'm pretty sure that Whiplash had to specially request them from the IEM manufacturer, or something like that. You can't just buy them off the rack. You can cut them off the old cable, drill into the contacts, and solder the wires there, if you know what you're doing. I've used cut and filed pieces of copper wire as pins, but it's pretty ghetto, there's no substitute for the real thing. This is probably going to be the sticking point for you DIYing one of these.
I wouldn't sleeve this cable, except maybe with some cotton or nylon multifilament, especially if you don't want it to be too bulky. That Piccolo cable isn't sleeved exactly, it's actually a super-tiny coaxial cable. I won't go into detail on what I think about using coax for non-digital cables. It basically has a clear coating over a metal braid, which goes over a layer of thermal tape, then the silver-gold wires are inside. If you go to wirecare.com there are a lot of materials to sleeve a cable with. Carbon fiber sleeving is something I do work with, but you have to layer it with something, either put it under PVC shrink (Techflex Shrinkflex, which makes for a very stiff decorative cable, not a good headphone cable option) or put it under 1/8" clear teflon braided sleeving from Techflex (a personal favorite). It is said to be a pretty good shielding/antistatic material although I don't have the equipment to test this. Don't get carbon fiber fabric sleeving/braided tubular sleeving confused with Techflex's carbon infused nylon sleeving, which is a conductive nylon sleeving that's got carbon built into the nylon strands - it looks like regular techflex but costs vastly more as it's a good shielding material. It isn't especially attractive. Carbon fiber sleeving that's sold by Techflex is awful, it flakes and fluffs and looks like crap very very quickly. The carbon fiber sleeve I use is from Soller Composites and it is very resistant to physical contact, it won't misbehave and develop tufts/flaws in its pattern when it's handled - it looks identical to the Techflex product though.
You probably don't want a Y-split as big as the Viablue for a compact cable like this. It'd look cartoonish on a naked cable like this, you don't need anything to cover the y-split and probably it would look best that way. The cable can't unravel without a y-split, that's not how a braid works. When you stop braiding, you simply take two of the wires and twist them into a pair, ditto with the other 2, and those are your earcup wires that go to the headphones. They end in a connector so they can't unravel.
PM me if you get stuck.
