If you can match the stain, you may not need to refinish the whole top.
If you're going this router try to determine what the finish is . If its shellac or wiping an area with denatured alcohol will dissolve the finish.
Many finishes can be simply scraped off. Definitely resist the urge to use a stripper as it may leak through the veneer and compromise the glue.
IMO grain filling is not necessary but will give a glass smooth surface. I've finished plenty of walnut and mahogany without grain filling and it looks fine.
Oh, and if you're thinking about sanding, approach with extreme caution, especially near the edges.
Sum it up, I would scrape the finish off with a card scraper, very carefully sand, restain (use an oil based stain just in case the veneer is hide glued), and top coat of your choice. Polyacrylic or urethane are probably your best most fool proof.
Last edited by DrRobert; 06-18-2019 at 11:04 AM.