The problem with sanding old finish is it quickly 'loads up' or clogs. This usually results in pressing harder to try to keep the sandpaper cutting. That results in loss of control. See where I'm going? Scrapers work much better.
Metal scrapers come in a limited number of profiles, but can be ground to shape to fit specific profiles. But, there is a learning curve to sharpening scrapers so they will cut well.
Another possibility is use freshly broken glass as scrapers. This is also historically correct. Visit a local glass shop & beg/buy some plate glass scraps (not tempered). Place the glass in a doubled paper grocery bag & break it up a bit with a hammer. The bags are to protect you from flying glass fragments. Sort through the broken pieces for one that will give an edge that matches the profile of the spot you want to scrape. NOTE: Be careful, there is nothing sharper then freshly broken glass. It's also a good idea to put tape on the edge you are holding on to, to protect your hands.
Hold the glass almost vertical to the surface you want to scrape & use short, controlled strokes. You should quickly cut through the finish & leave a nice smooth surface on the wood. The glass, being brittle, won't last long, so just find another piece to continue & break some more when necessary.
Finish remover is fine for furniture with large flat surfaces, but still must then be all removed before the new finish can be applied. It can be a real pain to get it out of the detail of carvings.
Paul