Polarised cord only works if your house sockets are wired correctly which is not necessarily the case and your earth bond might not be as good as you think it is. Always assume that the lowest competence is applied when it comes to safety evaluation.

At this point I wouldn’t run one of these things at all. If you drop dead you have no idea if some relative is going to plug it in and kill themselves with it. They were designed to a cost target when safety wasn’t a business concern. Steal the tubes and variable caps out and dispose of the rest. At best, stick it in a museum, preferably of dangerous things that should never be plugged in.

There’s plenty of tube kit out there you can buy which isn’t even remotely this dangerous.