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Sorry, but "Wanderschaft" is a rather old fashioned word for hiking. It is the noun version of the verb "Wandern" (to hike).

The stick is called "Wanderstab" or "Stenz".

"Wanderschaft" is the German noun used especially for the carpenters journey.

Actually, it is not `the' noun version, but `one' noun version. The more common contemporary known is Wanderung.