I'd scrape and use a magnet to pull filings. Alternate them maybe.
Also--a normal set of steel scrapers for woodworking are very cheap and last for decades. I prefer them now over all manner of "substitute scrapers", but they do require learning how to form and turn a burr for a proper edge. Paul Sellers, as well as many others teach this on YT. Folks do it differently, I do it the way that works best for me. I've also made scrapers from whatever scrap of steel or stainless that feels right and has a good shape (or make a new shape).
I just checked. The set I bought was under 20 bucks and was not the Blue USA sets you'll find if you look. Mine were from England (Sheffield of course) and may be a bit different than those "DFM" ones. I'll likely get a set of those to try (more scrapers-less looking for the scraper!). I use them for so many things and so little sandpaper any more. Scraping uses a long-lived tool, cuts down on waste, and eliminates most of that fine wood dust that gets all over everything.
You've fine advice, I just wanted to throw in a bit of info. Good luck with it.