This might sound like Captian Obvious speaking... but have you considered trying out the N3 and N5 universals? Either by scoping out a demo set or by going the momentarily more expensive route by buying and re-selling a used set?
^^ That was the cable I used it with. 4 strands of 28AWG SPC. It struggled a bit to grab all 4 braided strands, but if the cable is braided you'll only need it to hold on to one or two strands. Glad I could help!
I use Linum cables, stupidly thin. But I do have a shirt clip that is able to handle big, fat cables as well. I stole it from a phone headset at work, but it's the same as the one shown here: http://theheadphonelist.com/ciem_review/m-fidelity-sa-12-custom-in-ear-monitors-review/
3M DualLock leaves zero residue - trust me, I've been through literally meters of the stuff. Love it, be sure to get the low profile version! Friend of mine has the Chord Hugo incoming and I sorta fear trying it with the AK120 II... I'm afraid it will A) cost me another kidney and B) drag me back to stacking.
Two words for you my friend: Shirt. Clip. Like these: http://www.ebay.co.uk/itm/5-Headphone-Earphone-Cable-Wire-Cord-Clip-Nip-Clamp-Holder-Mount-Collar-Lapel-B-/231061654111?pt=LH_DefaultDomain_3&hash=item35cc590a5f
Thanks to the efforts of one of the best smugglers on Head-Fi, I am now the proud owner of a Vanuys AK120 II case, something otherwise exclusive to Japan. It's a bit on the large side though, slightly wider than it had to be. I actually think that you could fit an AK240 in it, but I'm fresh out of those so I can't test my hypothesis.