You can move all the images to the new external drive which will lead to images being shown as missing in the Lightroom Catalog.
You can then easily relocate them all by choose main parent folder > choose Locate > choose the folder at new location.
You can refer this article for relocation : How to find missing photos in Photoshop Lightroom
If you give the new hard drive the same letter as the original HD, and your file and folder structure is unchanged, then Lightroom should recognize the photos.
You want to COPY (not move) your photos to a new hard drive, then reconnect using Update Folder Location command, and then once you are sure everything is working properly, you can delete the files on the original HD. More details in Part 2 of this document: Adobe Lightroom - Find moved or missing files and folders
Thank you for confirming my thoughts on this and also providing the additional information.