Use really sensitive ones. The dose from a single scan won’t be much, as the beam energy is low and the power is pretty low as well. It will however add up with more expositions.
As a data point, when I went to the Chernobyl area, a day in The Zone including a few hours in the inner zone and a brief walk in the Red Forest did not show as any dose on my thermoluminiscence dosimeter (we borrowed one per each expedition member). I don’t remember the sensitivity of the thing but the total exposure we got was below its threshold.
As another data point, cosmic radiation during the flights. It is pretty significant, in comparison with the background, and is often delivered for hours at a time. Still not too much of a dose.
But worth poking into, if only to annoy the Fear Industry.
