Can I transfer my Non-Immigrant visa extension to a new passport at Don Muang airport or do I need to go to the immigration office?

I had recently to issue a new passport and in the old one I have a two month extension of a Non Imm visa based on marriage, an extension that expires in a few days. I plan to travel before this date to ask for a new 3 month visa in some Thai consulate abroad but before that I have to transfer the extension stamp to the new passport. I can do this for sure in the airport before I leave or I have to do it in CW immigration? I don't mind to go to CW to be sure but they gonna do it or they will tell me to do it at the airport instead? In case I can do it in the airport how long it takes? Keep in mind that I will fly from Don Muang airport NOT from Suvanampumi. Can they transfer the extension there?