Actually the battery charger made from a row of cocoanut shells and wires and whatever was in them was one of the few things the professor made which could conceivably be done in real life.
Now making a geiger counter out of cocoanuts and bamboo was a bit much even for a show in which you had to suspend reality.
Maybe not a geiger counter, but he could potentially make an ion chamber detector if he salvaged some transistors from the boat’s radio.