A copy of the member’s email body is attached to the admin email. But some additional messages are also attached at the top of the admin email which you should be able to customize from the language file. Please open the language file and search for the following line:
A new member have registered. The following email was sent to the member.
Once you find it you can change it to whatever you want.
Please have a look at the following post on how to customize the language file: