As long as your edge is formed properly, you could use compound loaded strops to refine your edge up from whatever stone you finish on.
I would, however, recommend staying away from using diamond stones (with the exception of the coarse ones for reprofiling bevels, with the caveat that you use a waterstone or something equivalent to remove the scratch pattern thereafter) as I and many others have noted that diamonds can tend to cause microchipping in very hard and thin kitchen knives.
Still, though, you will likely end up with a slight convex using strops. You won't see much benefit from moving past 4 - 8k JIS for a general purpose kitchen knife like a gyuto, so a 15K+ stone will probably be overkill for you unless you are sharpening something like a yanagi.