Let go of the grip of the conscious critical mind by confusing and tricking it into submission, prevent that part of the brain from relying on the safe tricks that it's developed in an attempt to produce a "good" or "impressive" style.
Comparison with a drawing of the same thing undertaken with your ‘usual’ hand will demonstrate that whilst a ‘wrong hand drawing’ won't, in all likelihood, produce a great physical likeness, it will produce a more emotive image.
Charm, humour and interestingness, this exercise will almost surely illustrate, doesn't come out of the sureness of style or habit that your usual hand gives but more than likely from this looser, more liberated, less dominant hand.