you have a few options
1. use JRiver to move the files (rename, move, copy). this only works good if you have no other files in the original folders other than music files (i.e. no cue, log, artwork, etc). if you do this, use "copy and update database". if there is other files in the folders, you can still use this tool and all the media files will be moved...if you keep the folder structure the exact same, you can then just do a normal copy/paste in windows and move the other files which will populate the original folders
**JRiver - once again a plea, to move all of the other files with this tool. many of the other file management programs do this, we all know it's possible...**
2. (what i use) turn off auto-import in JRiver (i always do for paranoia issues LOL), copy the files to the new drive, KEEP THE ORIGINAL FOLDER STRUCTURE (don't rename anything yet), then in JRiver select all the files and choose "update database to point to new location" and simply use the "find and replace" checkbox to change the drive letter. I've done this multiple times and there is no rescanning or anything as long as the new folder structure is the exact same, just the drive letter change.
3. there is probably even more ways to do this, but i use 2. somewhat frequently and never have issues
if you have a lot of files, do yourself a favor and download Teracopy. it's free, much faster than windows copy, and has a lot of options (like verifying the file move, pausing the copy if you want to use your computer for something, etc.). and always copy, never cut/paste....one never can be too careful with their precious media files