Disable email user notifications
One of the easiest ways to make sure no emails are going out is to add 

Mailcontrol (https://www.drupal.org/project/mailcontrol) which lets you specify what emails go out. 

or 

Maillog (https://www.drupal.org/project/maillog) which logs all emails and has an option to not send any emails to users. This will prevent all emails from leaving the system and log them if needed. It was designed to test sites but works well in this use case also.

Your other option is to go through and handle them one by one via code. There is no easy button inside of Drupal that will just turn off the service that I know of.

Sorry to just recommend a module, but given your needs this seems like a pretty obvious choice.