Is there space for an explanation? If so I would probably check yes and then write something like: "Two minor misdemeanors, over 30 years ago, no convictions".
From what I heard, in some States you can legally answer "no" once the statute of limitations have expired or if the record was expunged.
I am not familiar with the laws in your state but if it is a "shall issue" State than I don't think you will have a problem. I dont know of any "shall issue" States that bar permits because of an arrest unless charges are pending or the case is ongoing.
It might be a good idea to ask this question in your state's forum.
I am not a lawyer this is not legal advice.