Have a search around for a 'Spinthariscope'.

Ancient technology, very, very easy to make and use. They won't calculate dose for you but indicate radiation reliably, use no power supply and have no shelf life. I bought one years ago for a couple of quid, they seem to have gone up in price but maybe I am looking in the wrong place.

Also an old paraffin (kerosene) lamp mantle may be used to check if a detector is working. The old Thorium type give off significant amounts of alpha particles. Since around 1995 yttrium has been used though which is not radioactive.