The method for the edges, using SiC sandpaper, is basically so the edges are less likely to round over as compared to using the more compressible green Scotch-Brite pad. With the sandpaper backed against a very firm or hard surface (wood or stone/glass) there's less compression under the pressure of the bolster. That'll help minimize rounding of the edges that would otherwise be caused by a softer, more compressible material essentially rolling or forming itself around the crisp edge under pressure.
I recommend the SiC sandpaper, mostly because it does the job very well with stainless steel, even the hardened stainless for blades. Aluminum oxide sandpaper should also work well enough, though most you'll find will likely be a lower range of grit choices. It's generally easier to find SiC sandpaper in a wider range of grit choices, from around 220-grit up to 2000 or higher, for the sake of working & polishing harder materials like metals.
BTW, your bolster pic looks like the job should be pretty straightforward & simple. No awkward contours to complicate it, so it should be pretty easy.