On these facts, it is extremely unlikely that you would be able to withdraw your guilty plea. It appears to have been knowing and voluntary, and it was a long LONG time ago.
On top of that, New York State does not expunge criminal records. Many other states do, but not New York. The disorderly conduct violation shouldn't be affecting your job opportunities, but the endangering conviction might be.
Obviously, nobody can advise you on an internet forum, and this is just general information. You might want to meet with a lawyer who has done this kind of work before, and explore all the facts to see if you have any options.
(This is not legal advice, and neither creates nor implies an attorney-client relationship.)