I have to wonder if adding a wire wrap for several inches below the axe head would unduly imbalance the axe which would not be desired for the sake of esthetics, but it does beg the question if adding a wire wrap would offer a bit more durability against edged weapons?
its not exceptionally durable, given something like that is only 0.5 or 0.7mm thick annealed steel wire. but it'd certainly offer some protection to sliding cuts, if not percussion impacts.
As for the handling question, there's a simple way to find out. Ductape a few pennies side by side, along each side of the haft, from head to wherever you'd like the wrap to end. flick it around a bit, see how it feels. if it feels ok, the steel wire will be pretty close to the same weight and distribution...