Pretty sure you can't add a custom toolbar button and none of the existing ones will do that.
The $30 Mail add-on
Mail Act-On includes rules for outgoing mail which might work for you.
Alternately, and free, you could create a Smart Folder to include the mail sent by you to a particular recipient. You could then move that mail to an IMAP/Exchange/On My Mac folder of your choice every once in a while.