I looked your device up online. It appears to be a wireless telephone headset.
It also appears that there is a button to push to connect it to your telephone line when you want to use it.
Years ago I had a Plantronics telephone headset. It looked a lot like the headsets that the folks at mission control used to use with the clear plastic mic boom. I had to remove the telephone gizzards from the base of the thing and replace the earphone with a more modern one out of a Walkman style headset, then it was pretty much a straight forward wiring job.
I'm not real sure how you would convince any components inside the base of the wireless headphone device you have that it is connected to a telephone line and it may have to be in order to work.
I've been looking at wireless headsets for Skype. They have separate plugs for the mic and the speakers. That should be easy enough to wire into your rig. Of course the rig might mess with the transceiver in the wireless headset.
I'd think of buying a lot of ferrite beads, then have at it.
Any tool is a weapon if you hold it right.
“The only difference between stupidity and genius is that genius has its limits.” A. Einstein