I understand you want to maintain the edge on your razor with stropping on leather, and when that no longer brings the edge to peak condition, a touch-up on a strop with "green paste". Is this green paste the Dovo green paste or a Chromium oxide based green paste? Both are green, but otherwise very different.
After a couple of months, your pasted strop no longer seems to be able to bring the edge back, and you are looking for a whetstone that can bring the edge back within reach of the pasted strop, right?
That is a much used strategy for maintaining a good edge on a razor, and probably one of the easiest.
A Chinese 12K stone will not be of much use for that strategy. It is more a type of stone that finishes the edge, than a stone you can use for bevel correction. Bevel correction is what you will be doing. A Coticule is quite capable to do that, but it won't be with 10 or 20 laps. It depends on the abrasive properties of the paste you're using and on the type of pasted strop, how much the bevel of your razor will turn into an arc after a couple of months of touch-ups. It is the belly of this arc, that the whetstone must remove. The more pronounced the arc, the more work you'll need to do on the whetstone.
I have a couple of returning "customers" (I don't charge them, so they are not really customers), that rely on this method, but bring in their razors for the bevel work on the Coticule. By that experience, I know it can take quite a bit of work, certainly when more abrasive pastes have been used for the touch-ups. The time it takes can be in between 5 and 15 minutes. It might be best to get a Coticule from a faster layer. (There are couple of different Coticule veins, and the main difference is the speed at which they can remove steel when used with an abrasive slurry).
Coticules are an ecellent choice for this kind of work. In fact, that have been used for that for centuries, by many barbers.
Kind regards,
Bart.