Polish your resume and hone your pitch. Take whatever reasonable steps are necessary to make yourself fit that job you’re applying for. But please, please, don’t trim your nose.
Even in this day of e-applications, a cover letter is a must. It’s a chance to show a little personality, make yourself human to the poor soul who is sifting through a mountain of CVs in search of the Mr. or Ms. Right for their workplace. You can show them your writing chops. At a minimum, it’s a chance to prove that you spell.