Complete refinishing of a 1920s case is a big deal. You will have to disassemble the case parts, which are stapled or riveted together, and replace the case covering. I have heard of people who could do this, but I have never seen the results in person. I don't think anyone would do it today for anything close to a reasonable price. I would be happy to be proven wrong.
My procedure to restore old cases from the 1920s, and I've done a lot of them:
First, buy a bottle of Fiebing's black shoe dye at a shoe repair shop. Completely cover the exterior of the case and all black parts with the dye (It will not look shiny)
Use a rotary tool or drill with a small rotary wire brush to clean all metal parts of the exterior of the case, including hinges, latches, locks and corners. they won't look shiny and new, but they will look clean and good.
Squirt graphite into the latches and locks. Don't use liquid lubricants, solvents, or oil. Clean up afterward as best you can.
Go over the entire exterior of the case with black shoe polish - That's wax, just like polishing shoes. Maybe do this before cleaning up the metal parts.
Leave the inside of the case exposed to the sun for as long as possible. Spray LIGHTLY with Febreze or light deodorant. Too much deodorant makes things worse.
I have darkened faded case lining by finding a permanent magic marker in the same color, usually blue or purple, and rubbing the marker onto an old rag, then rubbing the rag onto the faded velvet of the case lining.
When doing these restorations, you will mess up your hands. Use surgical rubber gloves to eliminate a lot of grief.