Instead of even using steam you can just do this :
1. Change the Key
2. Open up the Arma 2 OA Directory (I assume you know the path, ill put it at the end in case you dont)
3. Click on _runA2CO
4. Game will open and key will be what you changed it to. You can make a desktop icon of the _runA2CO to ease running it.
If that doesnt work (did for me) Im sorry but i know nothing else.
Directory path :
Computer > Local Disk (C: ) > Program Files (x86) > Steam > Steamapps > common > arma 2 operation arrowhead