steps to hide your shut down button:

You can hide the Shutdown button from the Start menu using registry editor and also restrict access to shutdown, if a user clicks on Ctrl+Alt+Del. 
Follow the given steps to hide system shutdown button from start menu:

1. To use this feature, you will need to be logged into your computer with
administrative rights.
2. Click Start button and type regedit in Run option then press Enter for next.
3.Here locate the location to:
HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion \Policies\Explorer
4. Here in right side panel, right click to create a new DWORD value with name NoClose.
5. Now assign number 1 to its value data box.
6. Now close the registry editor and restart your computer after any changes to go into effect.
7. But next time, if you want to unhide the shutdown button then simply change the value data box to 0 or delete this DWORD item.