I know a way to access System Settings with FBI (not sure if it works if you deleted system settings though but it's still worth trying)
1. Open FBI
2. Go to "Titles"
3. Find the title called "NINTENDO DSi™"
4. Launch the title
5. It should take you to DS Wi-Fi settings then you can exit it by pressing B and it should take you to System Settings
Edit: then you can go to Other Settings and try to do a system update