Hobodozer, you have two solutions that you can do.
1. The best way. Connect any blu-ray drive (loan it from a friend? Buy a new one?) to your PS3 and update. It does not have to be married.
2. The easier way. Install a blu-ray checks removed firmware via option 6 from the recovery menu. It stays on "checking for update" for a long time, since it tries to look for an update on a blu-ray disc. Wait it out. It will probably take around 30-60 minutes, but eventually it will recognize the update on the USB. You can then proceed with updating.