Isn't there an offline version of waifu2x?
But more importantly, I don't know of a way to batch convert the luma / chroma combination process. Extracting the luma is easy however - just batch convert to 256 color greyscale.
I wouldn't be surprised however if there's a way to combine separate luma and chroma sources in video editing, and assuming that one can in fact do that, you can then cheat and use the video editor as a re-purposed batch converter (though this might only work if the resolution is consistent, and it probably won't work with anything that has alpha transparency either).
I imagine the process would go along the lines of importing a folder of images as individual frames, doing the theoretical chroma separation process, then exporting to some sort of lossless 4:4:4 format. From there, you open the greyscale WebP images as individual frames, then do the theoretical chroma combination process with the lossless 4:4:4 chroma "video" you previously exported, then finally export the final project as individual PNG frames in 4:4:4 chroma.