I’m not any expert here but can comment based on couple of things that I saw on few other threads on this web-site itself. IRCC give you an option to go for an upfront medical test (even before applying PR/work visa) and some of the panel physicians do provide the guard/protecting shield for pregnant women (during x-ray) to avoid/limit the radiations. It’s worth visiting panel physician office in person and talk to doctor and then take a call.
If you are applying “together” and one of you wish to complete all the tests EXCEPT X-ray, entire PR process will be kept on hold IMO. Technically, such application is incomplete to get further processed. Panel physician office submits some specific form to IRCC which indicates why the check x-ray is delayed. Again, I am not Immigration expert, Others can correct me if I am wrong. Good luck mate!