My main consideration would be battery life; I would be very happy with low lumen output as a tradeoff. The Fenix LD01 on my key ring would work quite well. It has a clip so that it can be attached to my hat brim if necessary.

While it is always nice to have a light, it isn't really all that critical, outside of being inside a cave. I would prefer not to travel at night, and at most I would use a flashlight intermittently, if at all. If there is a full moon or good starlight, I doubt I would use a flashlight very much. I would prefer to wait for daylight to travel. Much would depend upon the nature of the terrain (cliffs? mineshafts?), my knowledge of the country, time of year, weather, and many other factors. One of the reasons I carry a Fenix LD01 is that with a lithium battery I can reasonably expect to keep it on all night if I need to hike. A second lithium battery is also EDC on my person routinely.

I have to capability to hike all night, but unless there were exceptional circumstances, I would prefer not to move in the dark. Travel is usually much easier during the day.