I would take the cabinet completely apart, it's no hard to do, it held together with screws even the part that holds the machine has screws
what I do to get away the cost of chemicals , the using those, and if it real bad or painted.
I use a knife blade and scrape of wood bare, Don't laugh this is the way rough wood was finished was back when before sand paper, I made my blades. There about the same as a old time butcher knife blade, these are just a blade, so a sharp straight piece of steel is what they look like. some are shape on fit the edges.
It sounds hard to do. it's not. normally once you get an area to the wood the old finish begins coming off every quickly, it is hard on the hands, because of the pressure it takes, but is way faster than sanding,, this scraping with a sharp blade leaves the raw wood very smooth, often has a shine to it, Then finish by sanding
I'm lazy and stay away from days of sanding.
anything that the blade can't get into, it's acetone and a stiff brush even those small wire brushs. but that a flat face cabinet you won't need this stuff.