The diamond hones will work for any steel (which makes them versatile above anything else), but you'll need to go very gently on the carbon steels like CV and 1095. Almost no abrasion-resistance in these steels, so the diamond will cut very aggressively. Unless you're doing a big re-bevel job on a large, thick blade, I'd recommend using only the coarse or finer diamond hones on these. I avoid using XC/XXC diamond hones on them. 440C has a lot of chromium in it, which gives it more abrasion resistance (chromium carbides). Diamond will work fast on it also, but not quite so aggressively as on plain carbon steels and simpler stainless. I've also noticed, because of the aggressiveness of diamond on simpler & softer steels, the diamond hones will often load up (clog) pretty fast when sharpening them. That's something to consider also; not that they won't clean up pretty easily.
For what it's worth, I've found silicon carbide wet/dry sandpaper to work very well on carbon steels and the 420/440-series steels. Also works well on D2 (which responds well to diamond also). The sandpaper is cheap to get, so it never hurts to have some on hand. Given a choice, I'd pick the sandpaper over the diamond for carbon steels (used some today, in fact, for this very purpose). I'm sure a silicon carbide stone would do well also, for these steels. Diamond really excels on the vanadium carbide-rich supersteels like S30V, but can often be overkill for simpler steels.