As you likely know, most American made vacuum tube valve radios are of the "hot chassis" design. Usually, the chassis itself is well packaged inside the radio cabinet such that the user won't contact it. Or the chassis isn't directly wired to the line, but connected with a capacitor to the line. This to limit shock current to something less likely to kill. These design rules were mandated more or less by our safety organisation test lab "UL" "Underwriter's Laboratories". They got stricter over time, but even the early rules were enough for most situations.

I noticed that Aussie valve sets almost always use a power transformer. Which is a good way to get isolation from the powerline mains, but expensive. I suppose it was a government mandated requirement.

American radios will require an external step down transformer to get 120VAC. I don't suppose those would provide isolation though. Unless it's a clock radio, it won't care about 50 vs 60Hz.

So, would there be any legal risk issues if I sold and shipped to Australia these radios, as I would expect them to be put to occasional use (I electronically restore my radios to they way they were when manufactured)?

The main reason Australian radios had transformers was due to our nominal supply voltage, that being 240 volts though there's more to it.

Back before the eastern states, and later most states, were connected with grids each state had its own nominal supply voltage and frequency. New South Wales, Victoria and Queensland pretty much settled for the British 240 volts 50Hz system. Western Australia adopted a 250 volt 40Hz system. South Australia and the Northern Territory had a bit of both the above systems though later adopted the British standard. I am not sure what went on in Tasmania though it'd be easy enough to find out. The Northern Territory, like Western Australia is sparsely populated and many towns run on diesel generators though the larger cities like Darwin and Alice Springs have a good quality electricity supply, again with 240 volts 50Hz.

The size of the transformer will end up dictating what frequency it will tolerate. Many radios made for Western Australia 50 years ago would not work for very long if fitted with a transformer designed for 50Hz. It would generally melt-down and require replacement. Radios sent to Western Australia at the time were fitted with larger transformers to account for the lower frequency. I have such a radio in my collection, an AWA Radiolette 500M with '40~' stencilled on the back of the chassis. It works quite well in the reverse situation though.

Now, if you aren't already confused then you might be soon. In addition to the AC electric light systems I've mentioned, Some of the state capital cities also had 240 volt DC mains so that things like lifts and escalators could run without the buildings they were in requiring the fit out of mercury-arc rectifiers and associated equipment. Before the last of the DC mains in Sydney was turned off in the late 1980's the Sydney County Council (now called Energy Australia) asked building owners to retrofit their lifts for AC operation which meant either replacing the machines or installting rectification equipment - neither option being inexpensive.

The DC mains was also available to many households back in the day though and because of this, radios that could run on AC and DC became available. One such model, which I own an example of, is the Airzone Radiostar of 1937, a tombstone shaped table model which I believe used a baretta as a current-limiting device and of course there is no transformer.

Like the transformerless American models you describe, these Australian AC/DC models are deadly if man-handled the wrong way, particularly if the plug or socket polarity is in reverse. What's more, the earlier radios didn't have a back on the cabinet. Apart from circuitry they were identical in every way to their AC-only brothers.

Whilst most owners would have been aware of the dangers and also remembering that we are taking about an era where children were forbidden to play with appliances the way they do today probably saved a lot of people from electrocution. Sadly the same does not apply today and quite a few collectors and TV tecnhicians have either been belted or lost their lives because they were not aware that these radios had a dark secret - a live chassis.

When restoring radios there is a lot of confusion as to what is required. Firstly, even though the Standards Assocation of Australia (SAI Global) is pretty much on par with UL, CE CSA and BSA with the implementation of standards there were no standards government the manufacture of appliances in Australia back then. It was generally upto the manufacturers and the common sense of buyers to make sure things were made to be safe and used safely.

One of the problems that now exists is that even though there is a nationalist approach to standards and how they are interpreted there are still different laws in each state of Australia that govern the sale of used electrical appliances and how they should be restored. Some states require a 'test and tag' on an appliance before sale however this is a patently useless exercise as a lead tag doesn't mean an appliance is safe to use. It just means that the mains lead has been checked for damage and an earth continuity test has been carried out between the earth pin on the plug and the exposed metal of the appliance and that the tests passed at the time they were carried out. Not to mention that if the radio restorer hasn't earthed the radio (which is not required in any state here) then the earth continuity test can't be done anyway.

Some states require a seller to possess a second hand goods dealer licence if used electrical appliances are sold on more than 12 days per annum. This licence doesn't have anything to do with safety, just raising revenue for governments who waste the money on things we and the politicians don't need or want whilst hospitals, roads and schools crumble.

One thing a lot of people get confused with is the Australian Standard (SAA Wiring Rules) for electrical wiring. This Standard covers the installation of hard wiring in buildings connected to a public electricity supply only and does not cover anything else. There are Australian Standards and also other requirements by a small number of Commonwealth Government departments such as Telecommunications (A-Tick) and (C-Tick) that do cover appliances manufactured today however even these standards do not cover any valve radios manufactured or restored here.

I doubt there are any legal issues that would prevent you importing radios to or exporting from Australia certainly nothing that Customs in either country would worry about. For a definite answer on that you may have to consult a solicitor though.