I have several radio projects that I have restored including an old Hallicrafters shortwave. If my wife were to string up a wire outside (I am disabled) could I connect multiple radios to it or would it not work?

It will work but each radio that hangs on the same line will suck a little bit of RF energy out of the common network even when it is turned off. Depending on your listening interests this may or may not be a problem- I'd say that it could be problematic if you will be trying to pull in weak, distant stations. For max sensitivity in that case you might consider making a selector box or plug-patch panel so that only one set gets connected at a time. That also would allow you to have a centralized switched-grounding point for the antenna lead-in so that in the case of a lightning "near miss" the energy can be diverted to ground rather than possibly vaporize your antenna coil(s).