Is there a quick, non-intrusive way to see what's under vinyl siding?
Vinyl siding has seams between the pieces. You can push/pull at one of these to make enough room to get a small pen light inside for a peak. You can also inspect around any protrusions like water faucets or vents. Lastly, you can get a special vinyl pulling tool that is a thin blade with a small hook at the end. It's designed to be forced between two pieces and pulled down to release the siding from the layer below. With a little pressure from your hand you and pop the two pieces back together without ever removing a screw.

Two things to keep in mind: if the siding is properly installed, what you'll likely see behind the siding is a weather wrap (e.g. tyvek). And installing siding on a stone surface is likely to leave hundreds of screw holes that would take a lot of effort to patch.