I made this transition about a year ago. Either using the external USB SuperDrive ($79 from Apple) or the "Remote Disc" feature to connect to another working computer's DVD drive, install your earliest games in order. The last game (the one you intend to play from) will need to be a digital download, so either order one of the newest EPs or re-order your last one as a digital copy. This will effectively turn your base game & all your EPs into digital copies and you will be able to play without the CD drive.
Fortunately, the release of Origin for Mac should make gaming on an Air much easier from now on. 🙂