that's not possible. you can't work as a physiatrist without being exposed. you can't live on this planet or fly an airplane without being exposed. The average person takes in a certain amount of "cosmic radiation per year" which is higher at higher altitudes, frequent air travel, etc. there are some good tools on the web where you can calculate the 'average' radiation you might get per year. then compare that to the 'average' dose of radiation you would get performing fluoscopy procedures, it's not much more. you are right though the risk of radiation over time is unknown. there is a term called stochastic' events where maybe because u get more radiation there is more of a chance that a radiation particle will knock out a DNA that will give u cancer. but there is no definite link that this will occur. not all fluoroscopists get cancer and as u know peopel with average radiation exposure per year get cancer...
but yes, you do not HAVE to do flouroscopy as a physiatrist. check with individual residency programs about what is required during your residency training. You can do inpatient rehab, consulting, you can even do outpatient rehab without doing flouroscopy such as peripheral joint injections, EMG's, PT/OT scripts, cancer rehab, medical pain managment, general outpatient rehab, botox injections, etc.