I don't want to tell them what I did.
See an attorney for help with this. Because you took intervention in lieu of conviction, if you successfully completed the program, the charges were dismissed and you have no criminal conviction. The court could have also ordered the record sealed, and you should have asked for that. A record of dismissal sealed under OH code section 2953.52 cannot be asked about in any application for employment, license, or for any other right or privilege in Ohio. If you are asked about it in violation of that provision, you can respond to them as though the events never occurred. See Ohio Code section 2953.55. You may be able to ask to seal the record now if you did not do so back at the conclusion of the program, though your problem is that the Board already knows about it.
Your current problem put simply is this: if you don't provide some kind of response to the board's query, that refusal will quite likely mean the denial of your license. You need something more here than just refusing to respond. If the record was sealed, then you can respond as though nothing occurred. If it wasn't, that might not be possible.
You really need to see an attorney in OH familiar with sealing convictions for help determining what kind of answer to give the board. You'll need to tell them something, probably, since leaving the issue lingering probably means denial of the license. But what you should tell them depends on the details of your case, whether the record was sealed, and the like. Get some help with deciding how to respond. This is too important to try doing on your own after your investment in your education.