I don't use a water based soap on my furniture.
wipe with mineral sporits....which will remove old was and greasy soil....but not sugar or milk spots. For those gently use awater based cleaner....Murphy's is good.
But don't wash your furniture with soap and water.....and Murphys is just that soap and water and will cloud certain finishes and wet the wood in spots where the finish is scratched or chipped.
I don't use it.
Linda c

Most importantly what type of finish is on the piece of furniture? Is it oiled or is it varnished?

It is varnished wood which is why I would not think mineral spirits would be safe to use on it.

Mineral spirits won't soften dry varnish nor shellac not laquer. But water will cloud shellac and laquer.

Go to WalMart & in the automotive center get a container of GOOP. Cheap & environmentally friendly. Mechanics use it to clean their hands, so you know it's safe. If your wood is really dirty, apply the GOOP with 0000 steel wool. If not, just use a rag, then wipe off. If your furniture isn't slick as glass, then reapply till it is.