No question that the 'right' way to do this would be to run a separate, 4 wire circuit from the panel (or perhaps a sub panel if the panel is full). You certainly could use a small generator transfer switch to be sure that the dryer was disconnected when you were connected and that might even pass inspection but inspectors don't like unusual things and, while this probably doesn't violate code, it isn't, AFAIK, usual.
One issue to consider is that older dryer circuits run just the two phases and the earth (ground) wire. It isn't kosher to derive 120 from a phase and earth so you would have to either use 240 volt for everything or derive 120 from a 240/120 transformer. I believe newer installations require that the neutral now be run as well.
As the question is not what I think, or your wife thinks or even what the NEC says but what your insurance company adjustor might think standing in the ashes of your house I would strongly recommend getting a licensed electrician to do this work. He would probably try to talk you into the separate circuit and that would be, IMO, a good thing. If you want to undertake this yourself, and the fact that you are asking this question tells me you shouldn't, at least have it inspected. Then, if the unthinkable happens, you'll be in a much stronger position WRT the insurance company.
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