In a way the answer is all of the above. You should definitely consult with an attorney to discuss the issue of cleaning up your record. You should disclose the offense to the airline because they will likely find out anyway when they do a background search. Charges don't go away after 10 years, that is the arbitrary timeline the company asks about. In many instances companies are less concerned about the charge and more concerned about the honesty of the perspective employee, so you want to get out in front of this. Although i'd never say give up on working for the airline, understand you are up against many factors...it is an employer's market when unemployment is high, so the airline can be a little selective and there is a lot of scrutiny for those working in the airline industry. Good luck.
You should contact an attorney in Iowa about expunging your record. You can answer this question honestly as they only ask for the last 10 years. Your 2001 arrest might come up in a background search. Being upfront might be your only choice at this time.