There is a box you can uncheck at the bottom of the email page to skip the copy to yourself.
The email will be sent to the address on file for the recipient without revealing your own email address to anyone except he guy you sent it to. The only way you will know if they got it is if you get a reply.
As Colby said you can also use the PM function. With that you will know when the recipient read it because it will move from your Outbox to the Sentbox.