It is possible to sharpen a recurve edge on a waterstone with a rounded corner, but having wasted my time learning how I prefer the Sharpmaker. It’s near enough to the same speed, more intuitive, and more difficult for a new sharpener to make a mistake.
Some jigs have rounded stones specifically for recurves; I know there is a Lansky set. I haven’t used one, myself.
I suspect almost all heavy use recurve blades, carpet knives come to mind, are sharpened using pull through sharpeners. There are shaped sharpening stones specifically for recurves historically used in trade work, but they’re going to kind of suck.
Perhaps not a useful avenue for you right now, but my best results on recurves have by far been from paper wheels.
I know you asked how, but if you end up with only a few recurves paying a pro to do it is a reasonable option. Sharpening recurves is a niche inside a niche. No method I’ve tried of doing it by hand feels elegant or “right”.
Scratch patterns are in my experience a little overblown, particularly at high degrees of polish. The sharpener they linked you finishes on ceramic, which generally is fairly fine.
Pull through sharpeners’ biggest problem is that they can’t practically get a clean, consistent apex that follows the sweep of the edge. To get close the housing of the sharpening material needs to be extremely rigid, the pressure used needs to be consistent and light, the angle of the knife in the sharpener needs to be consistent from pull to pull, and the sharpening material needs to be very clean. Otherwise the act of sharpening, while perhaps polishing the bevel, drives the apex into steel residue or abrasive or shifts its angle. That will round, grind down, or rip tiny chunks out of the apex. Still gets a pretty sharp edge.
I don’t find pull throughs suffer much with regard to retention. They don’t get a knife as sharp initially, so they do start with a shorter clock. But from there retention is okay. They completely avoid wire edges, which is nice, so in inexperienced hands in a way they much improve retention.
For most knife steels and uses, pull through sharpeners are okay when used with a light hand. What I’m calling a “clean, consistent apex” isn’t practically necessary in pocket knives. The Sharpmaker and several cheap jigs can produce edges like that, though, and those edges definitely feel better in use. At the reasonable additional cost that’s worth it to a lot of people.