You can purchase an add-on which unlocks an option in Settings > Backup & Restore that will export Opus and your configuration to a USB stick as a portable version.
The add-on is AUD$10 and is in addition to the main licence, so you can use Opus on your main PC and on another via the USB stick simultaneously, and move the stick between PCs.
The portable version can be used without installing or admin rights.
You’ll still need the normal version installed on a PC somewhere in order to create and update the version on the USB stick.
There’s also the option of using the USB stick as a dongle and copying the portable version to a harddrive or network drive. It still won’t require installation or admin rights, and will still need the USB stick to be plugged in, but can run faster via a HDD if the USB stick/port is slow.