The carbides in 440C are all chromium carbide. As such, I personally wouldn't worry about them tearing out, as they're relatively easy to grind and shape with any man-made abrasive of AlOx or SiC (or diamond, obviously). If your emery cloth is true to the definition of 'emery' (i.e., 'emery' is historically 'natural' aluminum oxide, but the term is often misapplied for SiC as well), it should be fine. I've personally favored SiC wet/dry paper over emery cloth for grinding 440C, as SiC cuts it much more cleanly. My own use of emery cloth leaves me with the impression the abrasive is more 'blocky' than SiC, and although hard enough, maybe not shaped so sharply as SiC or diamond, and therefore doesn't cut as cleanly for the sake of the edge's crispness. It takes metal off easily enough, but leaves the edge in a lot rougher shape afterward (very heavy burring, for example).
For all it's chromium carbides, 440C is relatively ductile at the hardness typically seen in such blades (mid-50s to 60-ish HRC), and I think generally less prone to anything chipping, or breaking out of carbides at the edge, per se. 440C is pretty easy to shape and refine at the edge with anything beyond simple Arkansas stones, without worrying about any such issues as carbide tear-out. And for polishing 440C, any decent aluminum oxide compounds like white rouge, Mother's Mag, Flitz or Simichrome can work really well with it. Diamond paste can work too, but isn't really necessary, to handle the chromium carbides in 440C or D2 and other similar steels.
My own impression of grinding, refining and polishing 440C is based on results I'd obtained on one of Buck's older 440C blades (Buck 112 'two dot' model), which were reputed to be fairly hard to sharpen at one time (back in '70s/'80s especially). I'd tried, years ago, to thin & rebevel that knife with Arkansas stones; it just laughed at them. I gave that up and shelved everything on that knife for many years. Fast-forwarding to more recent days, I retried the same task a few years ago, with wet/dry SiC paper (ate the steel for breakfast), following that with polishing on a hard-backed denim strop with aluminum oxide compound (white rouge, or maybe Simichrome). The results blew me away, as compared to the impression left from the Arkansas stones. Easy, easy all the way.
David