Although I like the superglue answer I can just imagine the IT guys pain when he needs to replace a broken headset.
I'd suggest a couple different things. One is an all in one type of case like Dell sells with the small form factor OptiPlex workstations. You can plug the device into the back and then put on the cover which can be secured.
The other option is to get a small lockable box with holes in each end. The holes would actually be slots so that when the lid is opened the wire can be pulled out (up). Attach the box to the desk and run a USB extension cable from the workstation to the box. Plug the headset into the extension cable and then close and lock the box.