I collect straight razors from the Victorian era and then add some steampunk style.
Traditional 'scales' (the pieces on each side of the razor) are made from celluloid (invented in 1848) or animal horn. Remove the old scales by clipping off the pins at one end with a wire cutter or use a Dremel tool to grind them off. Try to keep the scales whole so that you can use them as a template.
I use exotic hardwoods from Woodcraft.com where you can buy it in 1/8-inch thickness (which is a perfect starting point). Trace the pattern for your scales onto the hardwood then cut it out.
Use double-sided tape to put both sides of the scales together, then sand the edges so that they match all of the way around.
For extra steampunk style, you can superglue or epoxy some copper to the scales as a backing, or hammer it first and put it on the front.
I've attached watch movements and various gears inside hollow cutouts in the scales, which I then fill with bar-top resin that dries clear and looks like glass.
You'll need pins and a spacer to complete the scales. Pins are 1/16 inch brass rods that you can pick up from Hobby Lobby. The spacer is a wedge-shaped object at the front of the scales that puts 'space' between them for the blade to fold into. It needs to be thin and angled. Just use superglue to hold attach the spacer to one of the scales.
Using a 1/16 drill bit, you can put holes for your pins in the scales. The washers around the pins can be obtained from Micro Fasteners.
Lastly, you'll want to cover the scales with a hard, waterproof finish. I use an oil-based urethane that gives a long lasting protective shine.
To pin the razor together, you'll need to insert the brass rod and clip it, leaving just about 1/16 on each side. Slide the washer on and then tap very lightly using a ball peen hammer until the pins mushroom over the washers and hold the scales tightly together.
For more help, you can go to the Straight Razor Place community or send me a pm.