Sandpaper isn't mandatory for maintaining the cutting edge on a convex bevel. I was sort of messing around with this yesterday, with a few of my convexed blades. A simple microbevel, applied with whichever tool is available, works fine. Don't touch the convex bevel itself, just do the very edge. This implies a slightly elevated angle (to touch JUST the edge), and a smooth, even stroke at very light pressure. I used my Sharpmaker yesterday, but exactly the same could be done with any other honing surface, same as any V-bevel. The slicing advantages of a convex are in the shoulders of the bevel, after all, which shouldn't need much maintenance at all (unless one has waited way too long to touch it up). The cutting edge is still just an edge.
And so long as you don't wait too long to touch up, simple stropping on any relatively smooth surface can keep a convex in good shape. That's how I've been maintaining the edges on my previously-mentioned traditionals. Rarely gone back to the sandpaper, unless I'm looking to deliberately thin the profile a little more. Wood, cardboard, paper, fabric, leather belt; all will work. Apply a little dust/fine dirt or other convenient abrasive to the stropping surface, if a little more bite is needed.