Running Romex from the generator to the transfer switch might present a problem due to vibrations associated with the generator. Solid wire in Romex can break at the connection points when subjected to vibrations over a long period of time. THHN run through the appropriate size non-metallic conduit might be a better choice.
I have used extension cords with the ends cut off to run 12-volt power in vehicles and trailers. The conductors are insulated, held together inside the sheathing, and are very flexible. I don't know if that's advisable for 120-volts, but if a good quality SOOW (the old SO) type extension cord is used, I think it might work.
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