I think it is a bad idea to use the WS-10C engines. Chinese carriers are smaller than US carriers as it is, so why only use large aircraft?
What you do need is a lot of thrust to weight ratio and probably a really lightweight aircraft. That would increase the payload capability on a STOBAR carrier. So the more advanced the engines the better. The Chinese already have access to the RD-93 and WS-13 for the FC-1 fighter so they can use that. I could understand it if there was a high-low combination of larger and smaller aircraft in the future but not right now.
In the future once they have the WS-19 they can switch to that. Another possibility would be a single WS-15 engine fighter. Since that would have high thrust to weight ratio and roughly the same performance as two WS-13 engines. It would also not require designing a new engine. But the thing is the Chinese are already developing a medium weight engine of the latest generation we even have photos of that. So at least it exists in prototype stage. Why develop an engine if you don't plan to use it?
To be honest I think the best option is a twin engine aircraft with large long weapon bays between the engines like in the Su-57. That would enable the inside stowage of large anti-ship missiles. The F-35, because it is single engine, has to have a huge box shape so they can store weapons below the engines which I think is suboptimal and increases airframe weight and drag.