If you move at a disciplined pace and always keep a close, controlling eye on the red creeping into your vision, you should be able to get through this part with no problems. At any forks in the path, simply use the matches -- they will indicate where the wind blows. If you see the red in your eyes go up whilst remaining stationary, quickly move up a few steps (off of the dangerous spot you'd be in).
Since not all of the pathways are connected, you should adjust the camera to a top-down view to find the easiest way. You will have to go through a series of QTEs that require you to press and hold one button after another until you make it through the space between the capacitors, and releasing a button too early will get you shocked. The number of buttons you'll need to press corresponds to the power of the capacitor. On the hard difficulty, this could actually be rather challenging; it is particularly important to pay attention and keep your composure while pressing the buttons. If you fail to go through a capacitor and don't think you're up for it again, try following a different route.
From a gameplay (non-story) perspective, there is virtually no reason to go through the "Coward" door, because getting shocked does not have many repercussions.