Trekking sounds ok in the context you describe. Ono to „trekking
je také mimo cesty“ není až tak podstatné, a co je to vlastně cesta
(HfE „není cesta jako cesta“) – road, trail, path? Podstatnější je
„long“ a „hard“, „over several days“ a (v daném případě) „po
hřebenu“ (along the ridge).
trek – dlouhá cesta, túra a long, hard walk over hills,
forests or mountains, usually lasting several days (HfE)
trekking: the activity of walking long distances on foot for
pleasure (Cambridge)
We really enjoyed our trek in the Tatras… We are still in
Slovakia, spending a couple of days in Bratislava after our
trekking. … As for feedback to improve the offer, I would
suggest that you provide a bit more information in advance about the demands and
difficulties of the route. It was a bit too difficult (long) for us given our
age and fitness and walkers who are used to trails in some other countries
(particularly the UK) would not expect the distances to take so long to
complete. When choosing the trek we looked at the Km figures
and elevation figures and thought they were within our capability. (travelslovakia.sk –
all these comments are from BrE native speakers)