As I said Laurie would know what to do about Dad's desk. She ended up first washing it with Murphy's Oil Soap. I knew nothing about this soap, as well... I've never seen a piece of wood I didn't want to paint. So care of wood furniture is new to me.
Instead of refinishing anything she scraped off sticky, dirty stuff in a couple places as well as some paper that was stuck to the desk. She thought the finish may have been a shellac lacquer combo. So she went over the desk with denatured alcohol. While there are some worn spots there is nothing that bothers me enough to want to do anything more to it.