The hankotsu is really a knife for dissecting beef / lamb and other land animals - even chicken. The back is flat (not concave) and the front can have either a convex edge or a short flat grind - I prefer a convex grind for this knife.
For taking apart whole fish, consider a traditional deba as an ideal choice.
"Id prefer to sharpen often to keep a sharp edge, than have to work with a semi sharp knife. " Exactly the way to think about it
So for both the hankotsu and the deba, an extremely refined edge is not required. The hankotsu edge should be robust and not too acute because it is used for chopping and shoving into joints. A 5k edge is fine for this. The deba can be a bit more refined especially past the heel area since the tip is used for fileting and the heel for chopping.
For your hankotsu, consider the Meara [natural] stone as an optimal edge and touchup stone. It is a fairly hard stone. Since the hankotsu has a fairly obtuse edge, it will be more easy to gouge the stone - so a harder stone is best. On the deba, a bit more refinement with a Yaginoshima Asagi is a nice choice. Both stones are easy to use natural stones and work together well.
I know going 'natural' early on is a bit unusual, but given that you have and will probably get carbon steel blades, these will be good choices.