There are a number of things you could do and yes, you could have the old speaker screwed down in some unused space in the cabinet and a new one installed just connected to the voice coil terminals of the old one, but thats kind of a kludge. Is the only thing wrong with the old speaker that the cone is damaged? That could be repaired fairly easily depending on the damage. What would be important is that the voice coil which is attached to the cone and makes it move, is able to move freely without rubbing on the central magnetic pole piece. It would be better to get the original speaker to work rather than trying to sub in a new one.
You say you get "static:" has the radio been recapped? Does it receive stations? It sounds like the speaker is not the only problem. What is the diameter of the speaker? Replacement cones are available and not that hard to mount. Need to get the radio working first and then worry about the speaker. If you can give an idea of what experience you've had with restoring radio electronics before, we can walk you through it. This ought to be a good radio fixed up.
