Hello,
Since the Registration Approval is switched on for Non-Members, there registration will go to Pending status as that is considered a priority Registration Rule (if Approval is enabled).
To make sure they do not recieve a Pending and Approved Notification, I would recommend you to divide the Invitation list for them.
Email are directly synced with an attendee's invitation list. If they in the same event however, on a different Invitation List, you can configure their email notifications separately. You can switch off both Pending and Approved notifications in that list and they would not recieve any such communication.
Also, if you are adding all the Non-Members at the back-end, you can just switch off both Registration Approval and Notifications.
All you have to do is add them to the Registration List and send them the Confirmation email whenever you want.
Let me know if you need more information on this.
Best,
Ankita Gupta