Kenneth / Jim,
The internet tells me: 303 Aerospace Protectant reduces fading and the non-oily, anti-static finish repels dust, dirt and staining. Unlike many products, 303 Aerospace Protectant does not contain silicone, oils, waxes, glycerin or petroleum distillates.
I looked up the SDS and most of the ingredients are listed as proprietary, along with water, ethylene glycol, magnesium nitrate and Glucitol. All Greek to me.
That being said, I have used 303 on my modern cars for over 10 years and have been happy with the results, much more so than Armorall. 303 does not leave the shiny surface that Armorall does. It will bring out the color a little. I have used it on dash tops and the inside door panels and so far none have split or faded even when exposed to the sun most of the time. My daily driver is outside all of the time and I have used 303 on it for ten years. All good so far. I use it as you suggest, apply it to a rag and wipe it on the surface. I have not noticed any problems with it harming paint.
I have NOT used it on any old car materials.
I have used the fisheye preventive in automotive paint and it seems to work. You should wipe the surface down with a surface prep designed to remove silicone residue first.