It's oil cloth, but not the kind made today, sadly. Contact cement is fine. For a refurb, take lots of pictures. Undo any screwed in components (usually the handle and a couple springs). Using a dremel or similar rotary tool, gently grind down the inside cap of each rivet. It's easiest to use a pin and hammer to knock them out and avoid damaging the wood rather than prying the hardware up. Set aside the hardware for cleaning. Sometimes they're split rivets (which I loathe) and you have to be VERY careful to not wreck the wood pulling those. LOATHE. Get the case WET. It'll soften the glue, make it far easier to remove and keep the glue dust out of your lungs. Pay attention to the order in which it comes off and where the various cuts are made. Scrub the case clean. Let it FULLY dry. Sand any uneven areas and patch what needs patching. Make placement templates in case you have trouble locating the original holes for the hardware. Ensure your rivets or attachment parts will work with the existing holes, modify if needed. Install the internal top and bottom lining. Install the hardware with a pop rivet gun. Put the outside upholstery on. Install the handles/feet/rest. Put the sidewall lining in. Seal any surfaces as desired. Done. If the wooden case is beyond repair but hardware is good, you can build a new case and use the same hardware provided the internal dimensions and hardware placements match the original. I'm mid process on two portable wooden cases or I'd show pics.