If I were you I would find out exactly how necessary the X-ray is. Can you just keep the cast on an extra week instead to be sure?
Found this online:
Question: Is it safe to have an X-ray during pregnancy?
BabyCentre Editorial Team: It depends on the type of X-ray you need and exactly how much radiation you're going to be exposed to. The greater your exposure to radiation, the greater the risk to your baby. Most diagnostic X-rays (dental X-rays, for example) do not expose the fetus to high enough levels of radiation to cause a problem. While fetal exposure over 10 rads (the unit of measurement for absorbed radiation) has been shown to increase the risks for learning disabilities and eye abnormalities, you needn't worry. It's rare for a diagnostic X-ray to exceed 5 rads.
For example, the amount of radiation that a baby gets from a mother's dental X-ray is only 0.01 millirad. Since a rad is equal to 1,000 millirads, one would have to have 100,000 dental X-rays for the baby to receive just one rad. Other estimated fetal doses are 60 millirads for a chest X-ray, 290 millirads for an abdominal X-ray, and 800 millirads for a computerised tomographic (CT) scan. For perspective, during the normal course of pregnancy your baby is exposed to about 100 millirads of natural radiation from the sun and earth.
Although the risk from diagnostic X-rays is low, experts often recommend that women postpone getting unnecessary X-rays until after giving birth. However, if your doctor feels X-rays are needed for your particular medical situation, it may ease your mind to know that the amount of radiation your baby will receive will most likely be well within the safe range. On the day of the test, make sure the radiographer knows that you are pregnant so she can properly shield you.