What is an alternate way to Switch Off mobile without use of Power Button?
There are some apps who have this feature, Like switch off, reboot and etc.

One of them is  Notification Toggler  , This app isnt particularly for switch off and reboot stuff, but you can do that also. :)

EDIT::

I think you have to root your device to use reboot and shutdown ,  You can't do it without Root unless applications are signed with the System Firmware Key. And playstore applications aren't that kind of applications that are signed with that. 

EDIT 2:

To root your Device , 
Check out these links,

Link 1

Link 2

Link 3