Q. How can I create a shortcut for Edge and Internet Explorer in InPrivate mode?
A. Both Internet Explorer and Edge have a context menu option to open an instance in InPrivate mode which is useful if you need a browser instance where you need to use separate credentials but its also possible to create a shortcut.
For Internet Explorer
"C:\Program Files\Internet Explorer\iexplore.exe" -private
For Microsoft Edge you have to take a different approach since its a UWP application. The solution I have found is to set the start page as InPrivate using about:InPrivate as the start page.