I’m not sure if double-edged safety razor are still available in the West, but here in Jingdezhen they are an essential trimming tool. These razors are thin, sharp, and most importantly flexible. Great for wheel-trimming details on small forms, or for scraping hand-built objects. The most used brand is Flying Eagle. I get the more expensive stainless steel ones. At 5RMB for a 5-pack, each blade is about 15¢ USD.
Using a Dremel or similar tool, edges of both thin and thick razors can be ground for specific uses, like scraping glaze off these plate feet.