Libraries and OneDrive are part of the system! You'll have to move them back to their default location in C: and then move them to the new external drive.
Well, I'd like to see this first-hand then, because this is not a windows issue; it is a Dropbox controlled error, as it is the deopbox app that will not let u install on a removable drive!!Actually, I think @nipponham and @mcsenerd are correct. The method that you are referring to and what I remember was for Win 8. This was, if I am not mistaken, changed in 8.1 (I remember this because this is what I did with my Surface 1 and 2 RT).
The question remains, however, can I just remove the current card and reinsert the new card and do what @mcsenerd has described? If yes, then it is damn cool because I will go and buy a 128GB MicroSD card today and just put the matter out of my mind!
I stand corrected. You cannot move the Dropbox folder to an SD card (as is), but it can be moved to an external drive like I have.
To get around this, you can mount the SD card as ChrisPanzer had suggested so it's recognized as a permanent drive, or you can move the Dropbox folder to the SD card and create symbolic links to the folder's original location. Another option would be to move the Dropbox folder to Documents (or any library folder), and then move that library to the SD card.