Is there any way that I can automatically email my drop shipper an order packing slip (without the customers email & phone number).

Maybe a good way to do this would be like how you setup the email confirmation in the configuration>email form but send a slightly different email (order items list and delivery address only) to the drop shipper.

I use a single drop shipper so it should be fairly simple!

Can some please help? I don't know any php?