Arkies are used with oil, Coti's water. You'd be better off starting with the Arkies, and using your Coticule as a finisher, not the other way around, IMO. Arkies are more associated with Tools, Knives, etc...Coti is associated with Razors. I have extensive collections of both. I don't use my Arkansas stones for razors, although some guys do.
I find I get a much smoother shave off a Coticule than any Arkansas stone. Also, I don't follow any specific method, like dilucot. You have to learn your individual coticule, every Coti is different, some fast, some slow...etc....

Save your Arkies for your knives, Use your Coticule for your razor, I think you'll be much happier....