X-rays are ok (per my OB) with double draping - as for getting numbed up, they recommend against novicaine (spelling?) because it contains epinephrine. A possible numing agent that does NOT include epinephrine is lidocaine.
I was given a local shot of that when I had a mole removal at 7weeks, and will be finishing a root canal (started pre-pregnancy) today and will use lidocaine (if numbing is needed) - I'll also be getting just one xray for the whole project, and my dentist prefers to do no more xrays during the pregnancy...