As a mountaineer you always have a versatile monopod available. With the right adaptor you can use it to take pictures.
A slotted PVC pipe slides on top of the head of the ice axe.

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http://www.hama.de/portal/articleId*2772/action*2563
or Novoflex.
http://www.novoflex.com/en/products/camera-support-systems/ball-heads/
but I don't think they are the cheapest.
Else try Google "ball heads camera mounts / tripods" or something like it.
To answer your questions:
* The slots fit tightly around the nose and the tail of the metal, but the lower section of the PVC pipe fits to the stem as well. I have used it with larger camera's and lenses without any problem.
* Bolted through the PVC cap and added a washer like this (see picture).