NOTE: The patch should NOT require you to register. If it does, it's an old version of the patch, which won't work and you have to download the versions linked above.
An alternative solution to patching the older versions of The Witcher is to claim the digital backup copy of the game on gog.com/witcherbackup (more info available here). The GOG version of The Witcher is fully updated from the very moment it is installed and doesn't need to be patched.