If you were convicted of anything, even a "small" misdemeanor, it's on your record. You can seek an expungement, but that will not "erase" it from your record - it will only add a notation that the case was dismissed pursuant to the appropriate Penal Code section. In your case, even an expungement doesn't do much, as it does not relieve you of the obligation to disclose it for employment as a peace officer.
The other thing is: You don't say what your "small" misdemeanor was, but you may want to verify whether or not you're disqualified from possessing a firearm. Some misdemeanor convictions carry a 10 year ban on possessing firearms under California state law. Those qualifying misdemeanors include things like assault,battery and any of the misdemeanor domestic violence charges (243 and 273.5). You can find the entire list under Penal Code section 12021.
From my experience with clients who apply for law enforcement, the police departments are VERY concerned with even the smallest of crimes. They usually want to the facts of the case and interview people familar with the facts around the situation.