To get any replacement parts for AKG phones, your best bet is to call up Frank, the current "parts guy" for AKG's parent company. You can email him to get price quotes on different parts and such, but it's much faster to just call him.
There's two different detachable K240 cables though. If yours connects via a mini-TRS plug like what you use to plug the phones into a headphone jack, you want part number 0110E0240. If it has a mini-XLR instead (three pins inside a metal shell), then you want part number 0110E0244.
This is the man to talk to:
Harman Pro North America
8500 Balboa Blvd
Northridge, CA 91329