I don’t have a stone basement, but it’s block, on a hill, with bare floor(rocks etc). We just fixed it all up with pump, membrane, dehumidifier etc. Get a good dehumidifier with an actual pump. Some say they have pumps, but they are super weak. Get a good one.

Before we fixed it up there was a decent bit of mold in the air. And things would collect dust then mold very quickly. So watch your stuff. Keep your nose open for mold.

Beyond that, every house is different. I wouldn’t have an issue doing what your trying to do. I’d probably just keep a door open when I was down there or something.