I agree that 10 half-lives (53 years in this case) is normally the standard but, my question is, was 1965 the last year these were made or were they available up to the 1970s or 80s as replacement parts?The half-life of cobalt-60 is 5.3 years. So after 50 years the radioactivity would be 1/1000 of the original activity.
@Dr.killjoy was right, the post office does screen for radio-activity and alarms actually go off. Assuming it was possibly less than 50 years old.
Normally, a DOT training class is required for Packing and Shipping radio-active or any other class of hazardous materials. The only way an average citizen can ship these materials is to pay FedEx to do it for you. Technically, they must come to your house to package and label it for shipping since you would have to transport it in your car to get it to a FedEx location. It costs about $100 to have them stop by a business location. I don't know if they even do it for residential service.