Is it possible to password protect a zip file created by Windows itself (without external tools?)

No, Windows does not provide this feature.

Have you considered using a portable app? You can install the portable versions of WinRAR or 7Zip to your USB, and use them to zip and password protect any file/folder you want. That way, you don't need to install anything to your windows machine.

There is a portable version of 7zip. No installation required. You can run it off your thumb drive.

Get it here

Or use portable PeaZip from the same site.