1. To stop the auto-update, do this: 

Using TextEdit, create a blank file. Then, go into the Format menu, and choose "Make Plain Text". 
Choose File > Save, and uncheck the box that says "If no extension is provided, use '.txt". 
Enter filename as "Spotify_new.archive", and save it in Your home folder > Library > Application Support > Spotify. 
Make sure to uncheck the box that adds an extension. The file cannot have a .txt or .rtf extension! 
Now, choose File > Save As, and save it again, in the same folder, but with filename "Spotify_new.archive.sig". 

Yes, you are indeed saving blank files -- that is correct! 

2. Make the files read-only and locked. 

Using the Finder, locate the Spotify_new.archive and Spotify_new.archive.sig files. They should be in Your home folder > Library > Application Support > Spotify. 
One at a time, do a Get Info on them (Command-I), and then: 
In the Sharing & Permissions tab, change access privileges to Read only. This is at the bottom of the get-info dialog. You will have to click on the little lock icon at the very bottom-right of the dialog and authenticate before you can do this. 
Check the box saying "Locked" under the General tab. 
Do this for both the Spotify_new.archive and Spotify_new.archive.sig files.