WORKAROUND:
Publish the Searches you intended for the Operator users to use, and add them to the Web Shared Overview Users group. The users would then only be able to see the published search from the Shared Overviews, and not be able to make any changes, just run the Search.
STATUS:
If the user (operators) has access to the Searches page in the Webclient, they will be able to delete a search configured with an alert. This issue has been fixed in version 7.0 and later.