When you say the original media files are not present, do you mean the installation files or do you mean the "c:\program files" folder for SQL express got deleted?
If you are just missing the installation files, SQL Express is free to download and you should be able to just re-download it.
If you mean you deleted the files instead of doing an uninstall, you are in for a bit of pain. The easiest way to fix this (in my opinion) would be to find a different computer (VM or physical), install the same version with as best as you can remember, the same settings. Once this is installed, copy the files from the new machine to the old one and then do an uninstall. If the new machine was a VM, then just kill that VM afterwards. If it is a physical machine, uninstall SQL express after this.
If that is not an option, then you are likely going to have a lot of troubles. Removing registry entries always comes with risk. It could be you remove stuff and it is gone from add/remove programs, but some little bits still exist and future SQL installs (express or otherwise) may be problematic. Or, a worst case scenario, you clean all the regsitry stuff up, but accidentally delete a critical registry entry and your computer no longer boots. No boot means you can't even recover the registry from a backup.
Editing the registry should always always always be a last restort (in my opinion).
Depending on what is all on this machine, it may be easier to just blow it away and start fresh?