Apocalypse in current usage means the end of the world. By that definition - no skill will be 'Apocalypse Useful' - because no one will be around in the aftermath of the end of time (with the possible exception of an intrepid band of our great grandchildren who might figure out how to jump between multiple universe branes at the precise moment of the 'big rip' - a very remote possibility imho).
Really what we are talking about are events that while devastating, are short of the level of destruction needed to end the world. The very nature of that definition means that there will be locations that are not directly impacted by whatever happened. The most key struggle would come from dependency on things that moved by long distance transport; various foods, fuels, technology, and other manufactured goods. As a result, local replacements would have to be found and developed.
In those areas harder hit - it would be very bad, if not impossible to survive after the initial event. I can see migrations of people from these 'hot zones' to more habitable areas. Refugees might put too much pressure on less impacted areas - causing a crisis in those areas. The first few years after the event might be very chaotic due to these population pressures and migrations. The very best way to avoid a humanitarian disaster would be to make sure all of the surviving zones have good communications - and plans in place for relocating and organizing the influx of survivors into their communities. I think you would also want to move as quickly as possible to restore technology to society - maybe not in the exact forms that we are used to - but restoration just the same. Having running water, food, medicines, heating and cooling, and energy in general are critical to sustaining life. As a result, I think all disciplines will be useful to society in that situation in one way or another. One example: artists and story tellers would be useful in bringing entertainment and beauty into the lives of the survivor communities - and might be very important in keeping human knowledge alive until information systems can once again be restored. Ultimately, people would be so hard pressed to survive that it would quickly become apparent that the survivors will do better by banding together rather than fighting among themselves.
Overall - I think if the event was large enough to depopulate the world significantly, I think the survivors would be very busy indeed, with little time or energy to waste of the staples of post-apocalyptic fiction: warlords, societal breakdown, and descent of our humanity to that of the animals, leading us to prey upon our fellow man. While there may be a few sociopaths who try to benefit from the situation, I expect the rest of us to quickly control that. Essentially, humanity has lived through these sorts of things in the past, and I am sure we would make do and get on with living in the aftermath of whatever mother nature sends our way again.