You should be left with the bare motherboard now. The next step is to take your USB extension cord and cut it roughly in half. You can save the other other half of the lead for future modding projects. Then, using a knife, remove all of the outer plastic. On the Corsair extension lead, it is also braided, so this needs removing as well.
The easiest way to do this is to pull it down so that it bunches up at the base. Once you’ve done this, you can just snip the wire at the base and the entire braiding will pull off. Sticking with the knife, you need to remove the outer plastic on the USB connector itself otherwise it will be too big to fit in the case. Try and keep a few big chunks, as these will be useful later for plugging up the disused USB port. I wrapped a little bit of insulating tape around the base of the lead, as there were a few bits left over from the braiding.
Next, you need to remove the rubber outside from the Corsair Flash Drive. With a bit of coaxing and pulling, you should be able to remove it without damaging it. It's held on with a similar glue that you find holding CDs to magazine covers. This should mean you still have a warranty should things go wrong. If you're not worried about warranty, you can always take a knife to it – but that does risk damaging the insides.
If you look closely where the pins connecting the battery are, you'll notice a hole that allows access to the top-side of the device. You'll also notice a hole just above this giving you access from the memory area. Thread the USB lead wires through both of these holes so that you end up with wires on top of the device. When the slack is removed, you'll find it doesn't interfere with the battery at all.
Next, pull the wire fairly taught and work out how much wire you should trim off. It's fairly easy to hide the excess – so think longer than shorter. But trim up the wires to a more manageable length.
If you're using a Corsair Flash drive, you can follow my colour pattern below. If you're using a different extension lead, then you'll have to do what I did – dismantle the other end of the lead to work out which colour goes where. Take your soldering iron, and solder the wires on. When done, use a little tape to just tape the wires out of the way. Feel free to laugh at my poor soldering.