To expand on mcknz's answer. It seems like there's mainly 2 options
- Yes, with an attempted brief explanation. As you mentioned, this may immediately disqualify you. And also as you mentioned, it's not like an interview where you can be personable.
- Lie. As bad as it sounds, I'd consider this the best choice. Not only because you won't get caught but simply because something like this from 20 years ago is just not relevant.
The choice is now up to you. Can you morally lie on a job application? Different people have different morals. I would have no problem with it.
If it makes you uncomfortable:
- Tell the truth
- Explain the best that you can
- Hope for the best.
Good luck to you :)
Edit: A very good point came up in the comments that, I think, helps with the morality of the situation. Employment history generally is thought of as the previous 10 years (or the most recent 7 jobs). So it may not even be a lie to exclude such information from a job application.