If I understand things correctly, if you set the payment option to automatically put orders into "Processed" status, then only that email is sent and the next status is typically "Shipped". If the goal is two messages, not three, that I think is the simplest way to go. The message sent in this scenario is the order confirmation (or processed message).

To do what you describe, perhaps you can edit inc_processorder.asp to remove...

 <!--#include file="sendmailCustomerProcessed.asp"-->

I have no idea if that include does other things. Another approach might be to still include  "sendmailCustomerProcessed.asp" but comment out the actual SENDMAIL call.

Good luck!