Mint Update tray icon is not in icon folder of any themes (or I don't know about it?), because of this to change this icon i replaced icons in apllet system folder, in my case /usr/share/cinnamon/applets/notifications@cinnamon.org/icons and you need to do this carefully and make a backup before doing this Icons that i replaced, in file "icons.tar.gz"
Credits:
- https://www.gnome-look.org/content/show.php/Win2-7+Pack?content=113264
- Xopek-Endurance (added symbolic icons for newer Cinnamon versions)