The license still needs to be activated through internet so you will need a computer/tablet/smartphone with an internet access and a web browser.
Open OmniScope on your offline system and open About window from the Help menu:
Expand Hardware ID section and then copy the text in the box.
Now you need to use your device connected to the internet. Open the following website:
Fill in your license email address and license key, then paste Hardware ID value (MAC-A28... from the screenshot above) in the 3rd box and hit Submit.
You Activation Code for the offline system has been generated. Now you need to transfer it again to your offline system. Open OmnIScope again, go to License / Register window:
In the "Activation Code" tab paste your code in the bit text box and hit Activate. Your offline system should be fully activated now.