The following commands will produce a small application that allows you to launch Vivaldi in Private mode on a Mac.
Start Terminal paste in the the following code (pressing Enter
when done):
mkdir -p Vivaldi\ Private.app/Contents/MacOS
printf '#!/bin/sh\nopen -a Vivaldi.app --args --incognito' > Vivaldi\ Private.app/Contents/MacOS/Vivaldi\ Private
chmod +x Vivaldi\ Private.app/Contents/MacOS/Vivaldi\ Private