Hidden Capture seems to be a tool you might have a look at.
- it records the screen
- it works on Windows *)
- it's free
- the "Hide and wait" button makes it invisible, i.e. hides the window. It will still be visible in Task Manager as a background process called
Be aware: when trying to download in a company, the website or the tool may be detected as "hacking tool" or "unwanted software". Your administrator might get a notice of this.
*) On Windows 10 I had some difficulties. The program was not able to write its settings file. Once I changed the security settings of the installation directory, it worked.
**) If not, it would need to be a kernel mode driver, not an application. Such things are much more dangerous and can cause bluescreens if not implemented correctly. If you like it to be less obvious, you can rename the executable.