No idea what 'ODNT zapper' is. Even a search did not show any useful results.
The Zapper is Stardock's uninstaller/cleaner
Moosetek13 has a point. If the missing log file causes a non-uninstall and the Zapper won't clean it... deleting the files shouldn't hurt
after deleting, you can use something like CCleaner (it's free) to clean up the registry before a reinstall (CCleaner will also make a backup of the entries cleaned if you tell it to)