I'm certainly not an expert on the topic, but I have used a similar process after having my hardwood floors installed. For most wood surfaces, I did a small area at a time with Murphy's (mixed in a bucket and used a well rung rag) and then immediately dried with a dry, soft cloth. The only thing I didn't use this on was a highly-polished wood surface. I didn't have any problems and it really helped get the dust and dirt out.

On the other furniture, I used olive oil and lemon juice (4 oz. olive oil and about 30 drops of lemon juice). Mixed in a spray bottle, spray on, rub, and dry with a soft cloth.

I've used Royal Guardsman polish, pour a little on a damp rag. like am old washcloth. It cleans all kinds of wood, don't use a lot of water and rub a lot. Dry with a soft cloth (I use old flannel diapers). Just my experience.