I found a solution that worked for me. Instead of having the email with the username and password be sent to the registrant, I tweaked it so that it comes to me. If I want to approve the user I then just forward the email on to the user. Here is a summary of what I changed:
In wp-includes/pluggable-functions.php
I changed this function on line 427 or so from this:
wp_mail($user_email, sprintf(__('[%s] Your username and password'), get_settings('blogname')), $message);
To this:
wp_mail('webmaster@mydomain', sprintf(__('[%s] Your username and password'), get_settings('blogname')), $message);
So the user does not get their username and password without me sending it to them. This could probably be turned into a plugin pretty easily...and would do it when I have some time.