iCloud Photo Library is not really intended to be a "backup" as once you make changes to the photos or delete photos, those changes/deletions happen on all your devices. So not a true backup service.
You can set up a second library to do what you wish BUT, you can only have ONE LIBRARY as your System Library and hence connected to iCloud. (I have two Photos libraries - one smaller one on my iMac's internal HD which is my "system library" and one larger one that is not connected to ICPL on an external drive - that I also backup to a second external drive.)
So, you can set up a new library, turn on iCloud Photo Library for it (it will probably come up with some message about having to turn OFF the first library as the System Library) and by enabling the settings for keeping all originals on the drive, it should download all your original files. However - that external HD will always have to be connected to your MacBook Air BEFORE starting Photos.
Another option is to keep your existing library on the internal drive. You can select numerous photos - perhaps if the external drive is large enough and you have the time - ALL your photos and tell Photos to EXPORT the photos. It will then open a window with options about the export (do you want the files as JPEGs or in the original format, etc.). Then a second window will open asking where you want the exported photos to be saved. Setup up before hand a folder on your external HD and select that as the place for the exported files. This will keep your existing Photos library exactly as it is - minimized size and accessing the photos from ICPL) and put all your photos - either the original files or JPEGs - on your external HD.