Here is an unusual shot of the bottom side of an original 427 Cobra with everything but the body removed:
This is typical of doing a "ground up" resto on an original Cobra. Removing the body will damage it, so normally you would leave the body panels intact, unless you had some so bad that they needed to be replaced.
The car shown here is CSX3178, Carroll Shelby's personal Cobra, that he has owned since new. This shot was taken at Shelby's shop in Vegas in 1997, before they moved to the facility at the track. The car is now Red with a 428, C6 automatic, and painted Sunburst knock-off wheels.
regards,
cobrajeff