It is very much like a sword scabbard, although for a sword stiffer materials would be better. I actually made a scabbard for a short sword not long ago using 1/8″ thickness luan plywood. I doubled the rail laminate forming 1/4″ thickness. For my blade this is to much clearance and it would rattle in the scabbard. Using a block plane I reduced the thickness tapering the rails to fit the blade. About 3/16 at the grip to 1/8 at the blade tip. This can be checked by laying the blade into the channel and using a straight edge across both rails. A little clearance is needed or the blade will jam in place never to come out without destroying the scabbard. To prevent the wood from swelling in wet weather, I coated the total inside surface of both sides with epoxy before final assembly and let it cure. I clamped the parts together before assembly to ensure the blade still slides in and out freely. Assemble the scabbard by gluing the scabbard side on with epoxy. After the glue dried I coated the outside with epoxy, with paticular interest in filling the open wood grain on the edges. As of now the scabbard is just painted black. Sometime or another I plan to cover the scabbard with black leather and a brass tip to eliminate wear. I need to decide how to carry the sword at that point and will probably attach it to a cross body shoulder strap.
Goodwill stores usually have old leather coats for cheap. I’ll buy one for the leather. Cut the scabbard cover and make ribbon for the grip from the coat.