On the Mac you've inserted the MacBook Air installer disk into, you should also assure you've turned on DVD/CD sharing in System Preferences. Do this:
1. Open System Preferences on the Mac with the DVD drive
2. Select the Sharing Control Panel.
3. Turn on DVD or CD Sharing by clicking in the box on the left
4. Insert the MacBook Air installer disk into the DVD drive
5. Go to the MacBook Air and open a Finder window
6. In the Sidebar on the left side of the window, click on Remote Disc
7. The Disc will mount on the MacBook Air's Desktop (you may need to click on an Authorize button on the Mac with the DVD drive)
8. Once authorized, the contents of the mounted installer disk will appear in the window. Click on the Optional Installs folder and double click on the Optional Installs package.
9. Once the installer starts, click on the triangle to the left of Applications, then check the Safari box below.
10. Click on Continue.
When the installation is finished, don't forget to turn off DVD Sharing on the Mac with the DVD drive. Also, you'll have to download the Combo Updater at Apple to assure all the needed Safari components are reinstalled. Get that at:
http://www.apple.com/downloads/macosx/apple/macosx_updates/
You could try just the Safari 3.1.1 updater, but if you manually deleted some key components, that may not be enough.
Good luck.