I am using “any file that is at hand”, provided it is flat, long and wide enough and still sharp (all my files are sharp, because I hardly use them). In the following steps, I refine that surface on my sharpening stones. I even tried to hone it on a leather strop, but that rounded the edges and I had to start from scratch.
In short, better files last longer, finer files reduce the time to polish the surface, coarser files produce a flat surface in less time. In the end, all that counts is to get back to work, isn’t it?
PS: That blog is mostly about saw files, which is a completely different application.