Let me correct you first. You have been charged and that will remain permanent, even if the charge is eventually dismissed. You would have to file for an expunction to remove the charge from your record, if you qualify.
As for your applications, most of the ones I've seen only ask if you have been "convicted" of any crime. So long as that is their question, you are perfectly in the right to answer "no". If, however, they ask if you have ever been "charged", you would have to say "yes", unless and until you are able to have the matter expunged.
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It is worth adding to Mr. Garrett's excellent answer that you are not eligible for an expungement if you were required to plead guilty as a condition of doing the program (which is usually the case for diversion programs like the 251 program or petit larceny diversion). Even if you didn't plead guilty, if the diversion program is a condition imposed by the court (rather than the prosecutor) than you may also not be eligible for expungement.