World Championship Winning Computer Chess Software Program & Downloads for Chess Databases, Analysis and Play on PC, Mac, iPad and iPhone — Visit: Hiarcs.com
In Windows they are stored in the registry (HKEY_CURRENT_USER\Software\HIARCS\HiarcsChessExplorer\Recent) so you can edit that if you know what you are doing.
One workaround is to move the database away for a moment and run HCE. The missing file should be removed from the list and won't be restored when the database is back.