Something to consider instead of an ice axe: Black Dimond Whippet- I have one of these and I love it. When you are crossing a steep snow slope, you really want to have your poles in your hands, people tend to just keep ice axes on their pack where they are just dead weight. Using this you still have your pole and you have a self arrest tool. It didn't bother me at all to have the pick on there while hiking. They used to make a model that was just the top segment of a pole and you used the bottom of your normal pole. It was called the Whippet Trek, but I can't find it online anymore.
Black Diamond Whippet Self-Arrest Ski Pole
Black Diamond Whippet Self-Arrest Ski Pole