I have the double edge frosts hook knife, with the bevel on the outside, and the way I sharpen it is this. Get your strop and apply a small amount of stropping compound (available at axminsters or quality shaving companies) and start on the part of the edge closest to the handle. Then, as you push the edge backwards down the strop rotate the blade anticlockwise (if you are righthanded). Do this 20 times on each edge and it will be razor sharp again. Be very careful not to roll the edge as you come to the end of the stropping as you will end up needing to buy a new hook knife.
The best thing about the frosts (apart from the low low price) is the edge retention - if you do this properly you will not have to do it very often at all (thankfully).