(Cleanest solution but you need to do this every time or create your own launcher for it.)

3.4 by launching Opera from the commandline with the switch -check-for-update-interval=0.(Both 3.2 and 3.3 will give you 'An error occurred while checking for updates' under 'About Opera') 3.3 by setting a system-wide proxy or personal firewall that blocks connections to Opera's update servers (only).3.2 by blocking the auto-update-server via /etc/hosts – (untested: 127.0.0.1 ?).(Giving you 'Checking for updates…' under 'About Opera' never finishing, otherwise it launches and behaves fine) 3.1 by moving/deleting/disabling the binary above – before the first launch.In this case Opera.app/Contents/MacOS/opera_autoupdate is run and auto-updates to the latest version while we still see the operating system verifying the application bundle. Obviously, parts of an application package are already executed while we all think macOS blocks all execution until the verification process is finished. The verify process for newly installed applications on macOS is misleading us. That gives you a drag and drop install from a DMG. Or for a fresh installation: download the full installer DMG from Opera's servers: The application is self-contained and will create all necesary support files on the fly when run. This can be circumvented by copying an old version of a fully installed Opera from a backup.

Like many vendors you may end up with a tiny download that is only an installer stub that pulls in the actual installation data at runtime. You need the actual application or the full installer Mounting a disk image is possible without internet connection. The screenshot in the question doesn't show the verification of the DMG on mount but the verification on application launch. There are a few problems to consider here:

Opera web browser older version