How can I swap Ctrl and Fn keys on a corporate computer?

It can't be done. Not without getting your hands dirty, that is opening up keyboards and swapping keys at the hardware level. Pressing the Fn-key changes the scancodes for other keys on the board, but is not reported to the operating system. For example, on a lot of notebook keyboards, pressing Fn-K will be registered as pressing an actual Numpad 2, even though that key might not physically exist. The operating system is fully unaware of any Fn-key and its presses can therefore not be remapped on a software level.

You can do it with Autohotkey. Download, install, and add this in the default script:

vkFFsc023::Send ^c

If this doesn't do, we probably have different keycodes (Because it works on my machine ;)). In this case, choose Open from AHK's icon in the system tray, then press CtrlK to view the key history, press fnc, then F5 to refresh, and change the vk and sc values in the script with the numbers in the first two columns of the row corresponding to your keypress.

You can do that for any combination of Ctrlsomething that you'd like to be remapped.