I agree but with 1 caveat: If OP wants to continue using the old drive for other things on the same computer, then it will be necessary to give either the old or new drive a different letter permanently. If the new drive letter must
remain different, then MC's
Rename, Move and Copy Files tool may need to be invoked after all, but just to simply change the path drive letter in the end, not to actually copy the files.
https://wiki.jriver.com/index.php/Rename,_Move,_and_Copy_FilesIn any case, save a library backup before starting, and
copy the audio files to the new drive rather than move them. The old files can always be deleted later if desired.

.
Be sure MC's Auto-Import is not watching either drive until everything is completed! When finished, confirm paths in MC's
Options > File Location.
One other recommendation: If you have any interest in preserving the old [Date Imported] field values, then for extra safety create a custom field and mass copy those values into it before starting. Also note that without special preservation precautions, the fields [Date Created] and [Date Modified] may be changed to the date of the copy operation since the operating system is involved. If concerned, you can check by copying a single test file and examining the result with the operating system's File Explorer.