10x raises a good point. Taking the cabinet apart first is a very good idea. It makes a huge difference in how easy it is to do the finishing work especially in the edges. Scraping and the acetone are also good tips. I've used single edge razors to remove paint splatters with very good results but haven't tried scraping an entire surface. Look up wood scrapers in wood working for more info.
The table surfaces are covered with veneer. Be very careful not to sand through it.
Either lacquer thinner or alcohol will both dissolve old shellac. Both will leave a clean surface ready for new finish and are easier than sanding. I haven't tried acetone. Use fine steel wool to rub the old finish off and wipe with clean rags. Work in a very well ventilated area, outdoors is best.
I would stay with traditional shellac (original finish), lacquer or a good varnish. All are easily repaired if needed. Polyurethane finishes are more difficult if repairs to the finish are needed in the future.
Rodney