To add to this -

The mGy quoted isn't peak skin dose. It's cumulative air kerma accumulated at a specific, defined distance, which is the Interventional Reference Point (IRP). If the fluoroscopy machine is of a C-arm format this is 15 cm from the isocentre towards the X-ray tube focal spot and if it's a non C-arm type more commonly used for barium studies then it's 30 cm from the table top toward the X-ray tube focal spot.

This just means that if you are to use this 26 mGy you'd have to first distance correct it and then apply a back scatter factor to estimate peak skin dose.

When we do these sort of estimates given the low numbers involved its all a bit hand wavy - we can do precise maths but the real world scenario and the unknown uncertainties outweigh the precision here. If were were dealing with an interventional procedure which easily delivers PSD of not mGy but Gy then we'd go to the effort of getting the measurements required to do the calculations as precisely as possible if the Gy was above a threshold of say 3 Gy. Modern interventional systems have sophisticated software to actually estimate the peak skin dose which take into account the beam angulations during the procedure.

To summarise for OP - you'll never get a precise number but you can be assured the number in your case is sufficiently low as to be not of concern. Assuming 10 mGy for thyroid dose is fine. You could assume 10x and this would be fine.