Yeah, i don't particularly like the name "wall wart" but everyone else on here seem to call them that.
Yep, there are AC versions too, which is what you want. A DC version wont give you a waveform to look at.
I really don't know how your flash units work but i would have expected them to use their own internal switchmode system to take the 230v mains and generate the 400v or so needed for the flash tubes.
Switchmode supplies do tend to clip the peaks of the mains waveform a little, however i doubt it will be a problem.
It is possible that your flash tubes use a voltage multiplier system to get ~460V from 230V, in which case yes they might distort the waveform a little from all the capacitance.
At some point you'll just have to plug them in and see if they work.
I would check your genny is producing a sine wave first though.
Any well designed product should be able to handle genny power without being damaged.
You should probably read up about earthing and generators as there are a few things that can cause problems if you have interconnecting gear running from generators and mains.
if I stuck a double adapter in the same socket as that charging the packs and used one side to charge the packs and the other running to an AC - AC wall wart then I'm presuming the waveform from the wall wart would mimic the waveform of the 240 circuit on the other side of the adapter which is under load?
Yes, the waveform will be the same on both sides of the double adapter.