You can set your another email at file :
app/code/core/Mage/Newsletter/Model/Subscriber.php
function
public function sendConfirmationSuccessEmail()
{
$email->sendTransactional(
Mage::getStoreConfig(self::XML_PATH_SUCCESS_EMAIL_TEMPLATE),
Mage::getStoreConfig(self::XML_PATH_SUCCESS_EMAIL_IDENTITY),
$this->getEmail(),
$this->getName(),
array('subscriber'=>$this)
);
add Following code for new email
$email->sendTransactional(
Mage::getStoreConfig(''newsletter/subscription/another_success_email_template''),
Mage::getStoreConfig(self::XML_PATH_SUCCESS_EMAIL_IDENTITY),
$this->getEmail(),
$this->getName(),
array('subscriber'=>$this)
);
}
This is for frontend customer subscribe to newsletter i am not sure that the same used for when admin edits the customer. I am still searching from where it send mail.