If neither acetone nor isopropanol are touching it, and if the vintage of the piece is late 1940’s / early 1950’s (I concur with 4yearlurker up-thread) then you won’t be dealing with shellac. You probably are also not dealing with a printed grain. It is likely a thin hardwood laminate onto plywood, probably finished off with a coat of varnish.
Still, you have the original finish and the patina, both of which you should try to preserve, else you won’t be able to match it when you re-finish.
I’d stay away from paint stripper unless you really do want a brand-new looking piece.
If the varnish is easily chipping off, I’d suggest a very, very, very fine sandpaper — wet&dry — in an orbital sander. Use plenty water and sand away. Keep the slurry on the piece, spread it around. When you figure you’ve got the varnish off, wipe away the slurry and have a good look-see.
The slurry will act as a lubricant, helping you keep from cutting too deep. As it is wet it will also raise the grain, which will in turn get cut down by the wet&dry. You should end up with a very smooth, very even-colored finish.
Do the carved bits by hand, if you must, or with a Dremel, or just leave them.
Once done, finish with a nice satin polyurethane or maybe even Danish Oil.
The dremel is good for repairing a tooth that falls out of a denture...then Crazy glue, but thats a whole other story..:O)