Simply use the email feature integrated in calibre. Instead of send-to-device or save-to-disk (which I assume you are using to export from calibre and open them in Amazon's Send-To-Kindle app) simply select the following option in calibre:
You will have to enter your email info into calibre, in Preferences ==> Sharing ==> Sharing books by email. calibre will login to that email address and send the email with the books from there.
And enter in the list of email addresses you would like be able to email to. Specifically, your send-to-kindle address, usually
your_account_name@free.kindle.com
You will also have to enter your email address in as allowed, at
http://amazon.com/manageyourkindle