My Japanese corner chisel is not the most handy tool in my tool box. In fact, I hardly use it. But since I have it, I feel obligated to keep it sharp. If you own one and look for instructions on how to sharpen it you will see that all of the demonstrations use flat abrasive stones or files such as diamond, oil, Arkansas, or a piece of steel wrapped in sandpaper.
The first challenge with this method is that you need to abrade the two bevels while keeping them at a right angle to each other and maintaining a constant sharpening angle for each bevel (30°), all while doing this freehanded! From my experience this is a challenging task. Sharpening is not complicated if your blade has one bevel and you lead it over a wide stone using a honing guide, or when relying on a hollow grind methods – if you choose the freehand approach. But trying to pass – and balance – a wide and heavy stone or a light and flimsy file on a bevel that faces upward is more difficult.