[Arran]

What I call a "Hot Chassis" set is an AC/DC radio where one side of the power line is connected directly to the sheet metal of the chassis, some companies did this because it was a cheap way to build, but most did not after the late 1930s.
The other way AC/DC sets are wired, and in fact are usually wired, is to have the B- independently wired and isolated from the chassis, with a capacitor and a resistor coupling the chassis to the B- wiring for RF shielding. Some call these "floating chassis" sets and this was how Philco, and RCA, usually wired their AC/DC model radios, brand Z less so.
  In my opinion rewiring the power cord with a polarized plug is a waste of time, almost invariably AC/DC sets, were designed so that the user would be insulated from the chassis under normal circumstances through an insulated cabinet, knobs, and a cardboard back. This is especially true when it comes to the floating chassis sets, they were designed to be as safe as they could be given the technology of the time in which they were built, later ones even had a safety interlock to stop people from poking around inside with the power cord connected.
 Now when it comes to the true "Hot Chassis" sets, yes they can be rewired to make them safer, I was attempting to do just that with one radio that had hacked up wiring underneath by running independent B- wiring from pin to pin, tube socket to tube socket, which was rather time consuming. I did find out a better way to do it though, I have a Belmont built Airline radio from 1949-50 where they ran a 6'' length of bare 16 gauge wire as a bus bar down the middle of the chassis, and connected anything that needed an electrical ground to it, I may try this trick on another set. The advantage to doing this is it curtails the likelihood of ending up with a dead short across the power line from something like a frayed antenna wire, not to mention reducing the shock hazard which is much higher when every piece of metal on the chassis is basically live.
Regards
Arran