You can email inside a password protected zip file renamed to myfile.mp4 or ideally some obscure file format it won't know.
Other than that, you could ask supervisor but I've dealt with business dweebs enough not to bother asking. I'd just bring some old laptop with smb filesharing plus a dhcp server running from the ethernet port and hook that ditectly into the work pc then copy the file.
Me I just clone tge corpoOS image, install promox then run shitty corpoOS in a VM and do my actual work on a VM without the bullshit.
If anyone asks anything, I'll tell them about my extensive gun collection.
Burn down the building before this big brother revenge of the nerd bullshit spreads.
But calling bs on that on tgat file header thing. They would have to even block text files. Many types of files have no headers.
And that shitty surveillance software didn't get a file header interpreter of every business useful file type.
Use your imagination, there are still dozens more ways to bypass IT security and make it look like that brown nosing colleague did it.
Just send the file as base64 chunks if you have too. Life without ditto clipboard manager should not be tolerated and neitger should big nerd brother sufferred to live.