As said, it's not possible to remap the Fn key on most PC keyboards as it doesn't generate a scan code. You can only remap the Fn+key combinations which can be done by editing the registry key HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Keyboard Layout\Scancode Map (except some keys that generate triple-byte scan code). Key mapping programs like SharpKeys or KeyTweak are in fact just does the heavy lifting of modifying the registry for you
SharpKeys is a Registry hack that is used to make certain keys on a keyboard act like other keys. For example, if you accidentally hit Caps Lock often, you could use this utility to map Caps Lock to a Shift key or even turn it off completely. This official release includes support for up to 104 mappings, an extensive list of available keys, and a “Type Key” option to help when managing mappings. As it relies on internal support within Windows NT, Windows 2000, Windows XP, Windows Server 2003, Windows Vista, Windows 7, Windows 8, or Windows 10 you must be running one of these OS’s for this Registry hack to work.
https://www.randyrants.com/category/sharpkeys/
So you can edit the mapping then extract the key to a *.reg file for use on all machines with the same keyboard. No 3rd software is needed
But the better solution is to persuade the IT department to allow the use of some 3rd party software like SharpKeys or compiled AutoHotkey scripts. After all, SharpKeys or KeyTweak is simply a registry-editing software and doesn't run any scripts, access the network or run in background. Just run it once and you're done, and more importantly SharpKeys is open source so everyone can verify what it does.
Update: you don't even need 3rd party solutions. Microsoft PowerToys is an open source 1st party software and supports remapping out of the box
Another way is to use Microsoft Keyboard Layout Creator and define your own mappings, but it may not work for all keys on the keyboard. After exporting the layout you can also use it for other PCs
See also Remapping via the Registry's "Scancode Map"