It sounds like you are about 90% done already. This is good.
Your NAS should show up as a path under /Volumes. If your share on your NAS is called "Music", then you should see /Volumes/Music/ and under that should be all the shared files on your NAS. To verify this you can use the Terminal and cd into /Volumes and have a look. Or more likely you will use Finder. In Finder use the Go menu and use "Go to folder". Type /Volumes and you'll see if it's mounted there or not. It should be.
Once you have found the proper path, then you need to tell MC that you have moved your files there. This is done with the Rename, Move, and Copy Files tool. RM&C is very powerful and can look a little intimidating. Take a few minutes, do some experiments, and you'll become comfortable with it fairly quickly I think.
The mode you want to use is "update database only". In this mode the operations you do only update MC's internal database. They don't move or copy any files. Just change the locations where MC thinks each file is. A vague outline of this is:
0. Make an MC database backup.
1. Select some files (maybe an album or two)
2. Open RM&C with Tools > Library Tools > Rename, MOve, and Copy files
A. Mode: Update database
B. Directories: uncheck
C. Files: uncheck
D. Find & Replace: Checked
Find what: /Volumes/OldExternalHD/Music
Replace with: /Volumes/NASMUSICFOLDER/
You'll need to choose the Find and Replace carefully and use the paths on your system for your old external drive and where the NAS music files are mounted in /Volumes.
Notice that the RM&C window shows a preview of what it's going to do before it does it. Adjust your Find and Replace parameters until you get what you want. Then try it on your test group of files. If it works, GREAT! You can do the rest. If not, restore your backup and try again.
Good luck!
Brian.