From my point of view it's okay to do that. I know a friend in UK who doesn't like to put his legal name in his CV, or LinkedIn profile either.
At the end of the day, CV is a tools to get you into the interview and not issue you with an official offer. Before a company issue you an official offer, thethey require you to provide them things like Social Security Number, Full Name, and few other things that you can't find in candidate's CV.
Having said that, if you get into an interview, and they ask you to introduce yourself, you can say: you are [Your Legal Name], butand your friends and colleague call meyou [Your nick name].