Your cgi program is very likely to keep its database on a seperate file on your server (not on MYSQL).
So what you need to do is to add a code in register.php to open this file and append the email address to the end of your file. However you'll probably want it to check the db if address already exists too, wont you?

Then this requires more work in your added code.
Instead of integrating your existing cgi program into vbulletin, I suggest to removing your cgi program and using a vbulletin hack which will mail your subscribed users whenever you need and move your existing email db to this new hack. If I'm not wrong there are good mailing lists addons hacks in this site.