iI am not sure what type of job or career you are seeking. I would not put a conviction on my resume or bring it up in a job interview. If questioned about it you can say you were convicted of reckless driving because that is the truth.
Read the questions that are posed by potential employers carefully. Doe the question ask if you have been arrested or convicted? The only real question that should be of significance would be convictions. Bearing that in mind, you don't want your absence of complete information in filling out an application could also be viewed unfavorably.
Very few employment opportunities will ask if you were arrested, particularly for a misdemeanor. However, those jobs do exist. Read what they are asking for. Have you been convicted of a felony? No. Have you been convicted of a misdemeanor? Yes - Reckless Driving. Have you ever been arrested? Yes. What were you arrested for? DUI. What were you convicted of? Reckless Driving. If it says please explain, say I was charged with DUI despite passing FST's. Therefore, I was convicted only of reckless driving.