That joint must be very tight even without the nut, because of the way the pulley sheave (where the belt rides) is cantilevered back over the body of the pump. Evidently at some point in the past, it was put together too loose, with only the nut holding it. Now the pulley has worked around until both the pulley and shaft are badly worn. As noted, you'll need to replace both of them.
If I were your grandfather, I'd want you to call for a flat bed. Even with the belt loose, there is too much chance of the pulley parting ways with the pump and doing even more damage (to the radiator, fan, hood, etc.) I know it's a pain, and probably more money than you want to spend; but a lot cheaper and easier than replacing that radiator !!
In my opinion, you are taking excellent care of the car. These things happen with old cars. The last time it happened to me (just last year in fact), I didn't notice the noise until after the shaft had broken. I was lucky, the pulley got stopped by the housing over my electric fan and didn't do any further damage. But it sure could have, especially if the stock fan was still in there.
PS, guess who put my pulley on without making sure it was tight without the nut :grumpy: