I'm wondering if I can just manually make copies of the registry files, save
them to a CD, and then if needed, manually delete the corrupted files and
just copy the archived ones from CD back to the OS folders?

I know there are all sorts of automated backup solutions -- I just like to
keep things simple and hands-on.

These are the files I would copy -- from Wikipedia:

The following Registry files are stored in %SystemRoot%\System32\Config\:

* Sam - HKEY_LOCAL_MACHINE\SAM
* Security - HKEY_LOCAL_MACHINE\SECURITY
* Software - HKEY_LOCAL_MACHINE\SOFTWARE
* System - HKEY_LOCAL_MACHINE\SYSTEM
* Default - HKEY_USERS\.DEFAULT
* Userdiff

The following file is stored in each user's profile folder:

* NTUSER.DAT