Bluetooth Receiver for Bose wired Headphones!

*** I didn't know where to put this, so I hope it finds some love in here ***

I have these AE2 Bose headphones that I received last christmas and I love them. Great quality, though admittedly I'm nowhere near qualified as an audiophile to speak of them in greater detail. All I know is I love them. They have a detachable audio cable with a 3.5mm jack at either end, and the headphones have a 3.5mm socket on the side.



So, I have been having trouble with the cable recently, whereby sound cuts off to the left side. I seems that the wire within the head of the cable is loose, and that I have to do some adjustments to get it working. I thought to myself that it was general wear and tear, so went to purchase a replacement from Bose. While searching their website, I noticed they have a new product out; the AE2w Bluetooth Headphones.



Now, they look almost identical to my AE2 headphones, but with a bluetooth receiver seemingly attached to the 3.5mm socket. I don't want to buy a new set yet, as I feel that mine have still a lot of mileage in them. So my question is; can I buy this bluetooth adapter separately? Or is there any other similar bluetooth audio receivers out there that could do a similar job. I have searched amazon and have seen a few, but almost all have either the dongle hanging from a short cable (which would be a real annoyance), or they probably wouldn't fit into the jack due to their design.

Any help in hacking my headphones and extending their life span would be appreciated folks.