Yes, with the correct tools one can remove the WiFi (AirPort) & Bluetooth board from the logic board. Follow this IFIXIT guide on the process and the needed tools [guide|16855|MacBook Air 11" Mid 2013 AirPort/Bluetooth Board Replacement]. In your case you're just removing it. You'll need to cover the cable ends with some electrical tape so they don't short out things when you put the systems back together.
With that said I think you're throwing out the baby with the bathwater here!
You can achieve the same effect by turning off the WiFi & Bluetooth services via the OS. To make it so someone can't turn it on (even your self) it quite easy. All you need to do is setup a second user account which you use which has the the services not accessible by the admin user. So you use this locked account all of the time and only use the admin account when you need to use these services. In addition using good user account practices: passwords, and if needed file or drive encryption on sensitive data.
Also remember the WiFi AP at your office will have needed setup & password settings so it just doesn't happen and the same also holds true for your Bluetooth services.
Lastly, one could still plug something into the USB port bypassing all of your efforts.