To hide shutdown option in start menu of Windows 10, we can use the GPO settings to deploy the following registry key and push it through group policy management:
Computer\HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\PolicyManager\default\Start\HideShutDown: change value to 1
Another way to hide shutdown button from start menu and found we can use PowerShell command to perform the task:
Set-ItemProperty -Name value -Path HKLM:\SOFTWARE\Microsoft\PolicyManager\default\Start\HideShutdown -Value 1 -Force
It could be safed as .ps1 then push as script through group policy setting as appear in below example snapshot:
Hope this helping you.