When you want to send a simple email from a Drupal template file, you can avoid creating a custom module or try to understand how drupal_mail() works. Sometimes it is just easier to fake a module call.
Basically, we are simulating the call of drupal_mail_system()->mail() from a fake module. With this method we avoid hook_mail_alter() and you can put this code whatever you want, even in a template file.
Just remember that if you need the email to be HTML, you have to change the Content-Type header to: