Equipment for documenting an adventure journey
I hate to burst your bubble, but if you are expecting video to be a similar level of intrusiveness to photography, you are almost certainly mistaken.  Video is a much more work intensive process as it requires constant attention to make sure you are getting smooth usable shots instead of the occasional random thought that "I'd like a photo of this."  It is going to take significantly more work and effort to get usable video footage that is stable and well composed.

That said, the amount of effort required varies greatly on what you are hoping to accomplish.  If a "reality cam" style video shot from a GoPro mounted to your pack or helmet and stabilized in post (will still be jumpy and move a lot) is sufficient, then buy a GoPro, a mount, some extra batteries and go to town.  

If you want something that more captures the feel of where you are with documentary like footage to make something that isn't a pure "action shots" montage, you will need considerably more effort to setup tripods, capture proper shots, more planning of the shots, plus the longer time it takes to get the shots.

Audio quality is also something to be mindful of in that situation, as shooting outdoors you are likely to have wind noise and will need to carefully monitor your audio while recording as well and getting decent quality footage might require multiple attempts at the shot.

If you can update your question with a bit more detail as to what you are trying to accomplish, we can probably refine the answer a bit more for your specific situation, but the key thing to know is that it sounds like your expectations of the effort required for a particular type of product may not be grounded in reality at the moment.