I have spent a fair amount of time off trail bushwhacking doing field archaeology and SAR, and I don't think any implement of this sort will be of much use in that sort of situation. You will find you want as slim a profile as possible. An ice axe or even a walking stick is likely to be an encumbrance. I particularly would not want to go around hooking rocky outcrops. Your hands are the best implements for that task.
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Geezer in Chief