Put the following code on your functions.php to get rid of the message on registration page. you do not need to touch the wp-login.php (so that you don’t have to worry about future upgrades).
function remove_password_email_text ( $text ) {
if ($text == 'A password will be e-mailed to you.'){$text = '';}
return $text;
}
add_filter( 'gettext', 'remove_password_email_text' );
Essentially you should be able to use a similar function on functions.php to get rid of any text
