On snowy ground and during the winter period an ice axe can come in handy, essentially for two reasons. As a point of support “uphill” on snowy traverses and as a safety tool in case of a fall.
In the first case you hold the ice axe in your uphill hand, with the pick pointing backwards. The spike is driven partly into the snow to give a third point of support (2 feet and the ice axe) and so improve stability and balance on the slope.
In the second case the ice axe can be used straight away, in case of a fall, to perform the self-arrest.
When your hikes never go beyond this level of difficulty, a classic ice axe with pick and adze and a straight, not very long shaft (50 cm... 60 cm at most) is enough.
The shaft should not be too long because, when you have to drive the ice axe into the slope just above you, if the axe were too long you would struggle to plant it in the snow. Ice axes that are too long are useless, if not downright cumbersome.
The ice axe used for hiking doesn't necessarily need the wrist loop (dragonne) of the one used for mountaineering on ice: an elastic sling fitted with a karabiner is enough. A single sling of this kind lets you pass the ice axe from one hand to the other every time you change direction. In fact, since you always have to hold the ice axe on the uphill side, changing hands with a dragonne would be more complicated.
In ice axes for hiking not much importance is given to the shaft as a whole. In this case we can't consider the shaft a handle but rather a stick to lean on.
It usually has a steel spike with a hole, should you want, for some reason, to clip a karabiner to it or fix the ice axe to your rucksack. The spike must be suited to driving the shaft into the snow without too much difficulty.
What is certain is that the function of the shaft of the ice axe in hiking is quite different from that in ice mountaineering, where the shaft matters less, since most of the work is done by the pick.