To set up an approval process for sending alerts you can create a role with limited access. The role would only have access to create and send an alert to the approver.
Once the Role is created the user can send an alert to the approver. Once the Approver has reviewed the alert they can forward it to its intended audience. This article will show you how to use the forward function in Mass Notification.
Instructions
If you haven't already, sign in to your site
Navigate to History/Reports
Select the alert you want to forward
Click the arrow icon in the top right corner and select Forward
Fill out the fields on the Send Alert Form, as needed
Preview the message and click Send