Your state does not offer much relief to defendants following criminal charges. You presumably know about certificates of good conduct and rehabilitation. Even a pardon won't do you any good, as you would not be requesting relief based on factual innocence -- it would not remove the disposition.
The age of the case and lack of records presents another complication. It is actually not unusual these days for records that old to be purged, with only a limited amount of information about the case retained by the court.
Sometimes a local lawyer can find a way to finesse a favorable disposition, with the help of a sympathetic prosecutor, but that's not something we can promise nor is it something you're going to find supported by statutes or case law. With your case already having been dismissed, I think it's a long shot (it would be under any circumstances), but I'm not seeing other options.

