The answer is simply to tell MC that you moved the files to a new drive. Use the Rename, Move, and Copy files tool to do so:
https://wiki.jriver.com/index.php/Rename,_Move,_and_Copy_FilesRM&C is a big tool, but don't let that worry you. Just read through the docs and do some experiments. You'll get the hang of it.
For this project, you want to use two specific things:
1. Update only mode. This tells RM&C that you've already moved the files and you just want to Update MC's database.
2. Find & Replace mode. This template, at the bottom of the tool, will let you easily replace the paths. For example if your old path was /Volumes/My Internal Drive/ and the new path is /Volumes/Big External Drive/ . You can use "My Internal Drive" as the Find and "Big External Drive" as the replace.
Notice that RM&C has a PREVIEW area to the right. Look carefully at the preview area and it will show you exactly what it's going to do *before* you press OK. If it's not right, adjust, and look again. Keep adjusting until it looks right. Only then do yo press OK to continue.
Do ONE FILE first. Then, once that works, do a few. Then do a bunch more (maybe all of them?).
Good luck!
Brian.