Crisis averted. The game runs well on my laptop.
In case anyone needs to do the same operation (Civ from desktop to laptop with no cd drive):
1. Copy the Firaxis Games (or just Civ4 I suppose, if you have more of their games) folder from Program Files to a USB stick.
2. Switch the USB stick to your laptop and copy the files to Program Files.
3. Download DirectX 9.0c separately even if you have a later DirectX. It'll run way better.
In case anyone needs to do the same operation (Civ from desktop to laptop with no cd drive):
1. Copy the Firaxis Games (or just Civ4 I suppose, if you have more of their games) folder from Program Files to a USB stick.
2. Switch the USB stick to your laptop and copy the files to Program Files.
3. Download DirectX 9.0c separately even if you have a later DirectX. It'll run way better.