The fan on my 26 touring has about 1/4 inch axial play. Should I be worried? I sure would not want to hurt my radiator, I live on a big hill and this car has never overheated.
That's a little excessive, add a a little packing (washer) to get it below 1/8". Of course you could put in a new pair of bushings. Another alternative is to rework and install ball (or roller) bearings.
Sounds like your felt washer/seal is missing or worn out. As long as the shaft nut is tight it should not fail catastrophically.
Does a '26 use a bolt for the axle? If so, has it backed out?