Wu Wei is simply a way of living without doing. How can this mindset help with job searching?
Consider your levels of stress, frustration, and exhaustion. Job searching takes a toll on your well-being and mental health. Allowing yourself to trust that things will work out can renew your motivation and energy.
The Tao of Pooh by Benjamin Hoff is by no means a job searching manual or a career advice how-to book. It's a philosophy book that aligns with A.A. Milne's beloved character Winnie-the-Pooh. The chapter "The Way of Pooh" discusses allowing for things to happen--effortlessly, naturally, spontaneously. In many respects, obtaining a job means relying on Wu Wei.
Tao doesn't force or interfere with things, but lets them work in their own way, to produce results naturally. Then whatever needs to be done is done.
Hoff recommends not trying too hard and allowing things to work out.
When job searching, consider taking the intuitions, the skills, the opportunities you are given and use them to your advantage. Do not waste your time and energy bemoaning why circumstances are against you. Simply let things be simple.
Learn to say "Oh Bother" and start over and over again. As The Beatles would say, "Let it be." Learn to let go.