Horn is an excellent scale material. Scales can be made very thin, which can make shaving and stropping easier. Thick scales can be awkward to handle.
The trick to finishing horn is removing the scratches at the low grits, 320. Scraping also reduces a lot of hand sanding, a good scraper can be made from a Putty Knife, Razor Knife blade or dollar store steak knife. A pair of scales can easily be scraped smooth.
Then sanded with 320, 400, 600 and 1000 or 2000. From 1 or 2k they will hand polish with any good metal polish, I use mothers then Maas or 3M Marine Metal Restorer and Polish. Pricy but a tub will last years.
Karlej, has an excellent Horn making, photo tutorial (How to make a tradition set of horn scales ... the way I do it.)
Also, study vintage scales for dementions and hole/ pin placement, you will find they are very consistent. There is a reason, it works.
Also, Lead wedges are traditional with horn, are easy to make and add balance to a horn scaled razor.
Nice work, for your first set, keep at it, it can be done completely with hand tools.