Here is a posible solution, allbeit a convoluted one, but one that could keep it sharp:
Apparently, because of the nature of gouging and carving, it is an activity which can potentially blunt a blade very quickly. I recently bought a carvin jack (a kind of swiss army knife for carvers) I didn't get on with it that much but the sharpening information that came with it was useful. Basically it said that, in order to maintain a sharp edge and protect the blade from microfracture when carving, it is important to strop the edge at regular intervals with a special polishing compound, rubbed on to a stropping device.
http://www.axminster.co.uk/product-Flexcut-Gold-Polishing-Compound-22340.htm
The stropping device designed for the carvin jack was simply a piece of wood with grooves matching the different blades on the tool, onto which you rubbed their compound like a crayon, there were grooves for the underside as well as the top of the blade. There was also a flat strip of leather on the 'slipstrop' for the large crook knife blade top as well as a convex form for the underside, which also accepted the polishing compound. I found this to keep the blade extemely sharp when used as they suggested.
I've also used the compound rubbed onto the underside of my leather belt for polishing my frost's clipper.
I'm sure that a strop could be improvised for the frost crook knife with a piece of dowel and some leather round it for regular polishing, and use the wet and dry suggested in this thread for main sharpening. The compound comes in a block £6.99 (SEVEN QUID ( I hate that .99 scam!) but it will last for ages and ages.
I also have a crook knife, although I'm not realy into carving and was considering building this suggested kit.