You can't without disabling Web Security Reporting. What you can do is enable anonymizing in Reporting Settings. This will hide the user names in reporting unless the person knows two passwords to deanonymize. That should solve the privacy issue.
If you still wish to have the ability to disable the Search Engine Report separately from Web Security Reporting, you can make a feature request at http://feature.astaro.com.
You can't without disabling Web Security Reporting. What you can do is enable anonymizing in Reporting Settings. This will hide the user names in reporting unless the person knows two passwords to deanonymize. That should solve the privacy issue.
If you still wish to have the ability to disable the Search Engine Report separately from Web Security Reporting, you can make a feature request at http://feature.astaro.com.