Wow, we're almost at two years from the initial post. Hopefully, it's gotten better. It would seem after 15+ with a clean record, for a misdemeanor, going by what you stated, you may be able to petition to have it expunged. Whether you can or cannot, it would depend on the state. You could check with a competent lawyer in the state of the occurrence and pay the one hour for a consultation.
If not, it would not just be your overseas license that puts you at risk, even your visa to live in said location in that part of the world requires a police report that demonstrates a clean record.
I also agree with Obbie, if you are caught lying while on the ground in the Middle East, the rules and protection that you enjoy in your home country do not apply. While nothing more may happen than your denial of visa & employment, it is a risk.
Your better bet would be to go somewhere where some additional dollars can make people look past these things, like flying Cargo from a base in the Ukraine. I met a CX Cargo pilot here, who left the Ukraine and totally regrets it. Not joking.