One note about ice axe's and walking axe's, and possibly trekking poles. Some of them can be loud when banged on the rocks. I once borrowed a Black Diamond aluminum ice axe for a sheep hunt, and the damn thing sounded like a gong being hit every time I accidentally banged it on the rocks.
There are walking axe's made by Stubai and Peltz, that have an extendable trekking pole out of the bottom of the ice axe. They are much quieter, but I question their durability. I used the Stubai version for a few years, and it was good up until the day it broke.
I have also used a Black Diamond Whippet, which is kind of a hybrid trekking pole/ice axe. I still have it, and it has served me well for many hunts and many years.
With that said, these days I use an old school wooden ice axe. Much quieter, and much more durable. They are pretty hard to find, but deals can usually be found on eBay.
One other thing I like to do with my axes/trekking poles, is make sure the metal tip is covered with some kind of rubber. When bouldering across the rocks in sheep mountains, the click and clack of the metal tip hitting the rocks is an unwanted noise, so before every hunt, I make sure to outfit my axe/pole with some time of rubber tip. I have found extra small hose clamps to be useful in keeping the rubber tips in place.