I would cut it back with 240g then a finish of your choice. A sanding sealer, cut back again then a few rubbers of button or garnet polish followed by a wax. A dark brown or black wax scrubbed into the carving with a cut down 1" paint brush will bring it up nicely. Do you have the escutcheon plate or is it missing?
This is what it should look like. If yours is missing you may be able to get one from Hong Kong which is where a lot of these coffers were made. I used to watch them being made in the workshops when I was a boy in Kowloon in the sixties!!!
I make my own M/C wax. I wouldn't use it on those carvings, I shall probably go for a softer wax as MrPercy suggests. Easier to get off.
I might try the top and see how the colour matches the sides then leave the sides with a wax scrubbing if the colour is OK. It's the flat surfaces of the top that are the ones in real need of TLC but they might stand out like a sore thumb if the rest isn't done - I won't really know until I start.
I seem to recall seeing the clasp, so maybe it's there.I've ordered a light brown wax and some button polish.