Hey Dave
That's a big and emphatic NO to using a steam mop on the roof. Just don't do it. The fabric on these roofs takes enough hits from cleaning/scrubbing; dirt; sunlight; stone impacts; repeated folding/unfolding, acid rain; cleaning chemicals and frost without adding to the list, so I for one would not advise you don't do that to it.
Also don't allow a pressure washer near it either unless its to wash it down from a great distance where only a misting will form and gently settle on the hood without any of the pressure blasting.
As for the Nenette mop, I have a good old-fashioned Nenette mop that I've had for years - I used it ONLY when my car was left cleaned polished, and waxed, but when after say, a period of dry weather, or the car has been left in the garage uncovered for a length of time, the inevitable dust had settled on it. Rather than wash the car again I'd give it a very light and gentle 'brushing' down to remove the dust.
However... These are mostly frowned upon in the detailing world because in brushing the car down with the Nenette mop, you are effectively dragging (microscopic) dirt particles across the paint which isn't ideal, and it's for this very reason that people now use snow-foaming to reduce the amount of physical action used against the paint when washing it, because the accumulative effect is that physical action will ultimately leave those microscopic skate-marks that you can see when you look across a painted surface in sunlight.
I'd say use it, but only when the car has been polished and waxed very recently and, don't use it every day.
I take mine with me when I show the 'modern' Midget, just to give it a dust down halfway through the day. To be honest though, the paintwork on the Midget is 39 years old now, and in need of some serious TLC so, although I still two-bucket wash it with a grit-guard and lambs-wool mitten, dry it with fluffy microfiber towels, and then polish it followed by a wax coat, the Nenette mop is not really going to add much damage to the already elderly paintwork in this instance, and as stated its only used at shows when its dry, to remove any dust that has settled on it.