Let me answer differently.
You can't file jointly unless you agree. That seems unlikely here. So you both need to file as married filing separately.
If spouse A does not include spouse B's SSN, spouse A can't e-file. They have to file by mail and attach a written statement explaining that they do not have their spouse's SSN, and they give the IRS as much identifying information about their spouse as they can (name, birthdate, last known address, etc.). This will delay processing and payment of any refund, and could bring additional scrutiny on both spouses.
This applies to you as well, if you file MFS, you need your spouse's SSN or you must file by mail and attach a written explanation.
