Do not show Mac Mail headers when forwarding, but do show in Inbox
The detailed Header view is a Menu bar Icon (you can set it up) that allows you to view headers from Received emails. 

To set it up right click on the mail menu bar and choose Customize.

From the new screen drag the "All Headers" icon to your menu bar.

Without some serious hacking, any email you send will also include the extended header information, same way as you can see it.