Batches of 1000 would be problematic-- smaller would work, but it would be painful.
If you have "Download Originals" checked in Photos>Settings>iCloud, then you can just drag the Library to your external drive, and Bob's your uncle.
But do you have "Optimize Mac Storage" checked in Photos>Settings>iCloud? If so, then your local library probably doesn't have full-sized images-- some may be just screen sized. In that case, you need to get the full sized images to back up. You can change the setting to Download Originals, and then try to force Photos to do Download the ones it's missing. Photos needs full resolution pictures when it edits or prints. You may be able to force a download by making of slideshow of all your pictures. Another method would be to print them all (not to paper!) to a pdf. You can choose to print; fill the page; print; then print to pdf. This will make a huge file-- you can put it on your external drive and erase it later.
Maybe the easiest way would be to make a new Photos Library, set it as your System Library, connect it to iCloud, and then let it automatically load all your pictures and albums and folders from iCloud. Then it's done. If your external hard drive is formatted in either APFS format or Mac OS Extended (Journaled) format, the new Library could be created on your external drive, and you don't have to move anything.