If outgoing port 25 is blocked you cannot send email because you won't be able to connect to the remote MX. What I would do is setup in a different hosting provider a machine that is allowed to send email and set it up to relay from your VPS listening in a different port (e.g.: 1025), then you could configure your sendmail to forward all the emails to that machine. To do that you need to add
define(`SMART_HOST',`relay:your.new.machine.com')dnl
define(`RELAY_MAILER',`esmtp')dnl
define(`RELAY_MAILER_ARGS', `TCP $h 1025')dnl
Apply that configuration and flush the queue with:
# ensure you have the package sendmail-cf installed
/etc/mail/make
service sendmail restart
sendmail -q -v
Keep in mind that sending those 9,000 emails will be sent from the other machine, so they might be considered spam or dropped by the destinations, but that's a different question.