WHERE do you click on Nexus Skirmisher?
The Skirmisher is a separate tool. You start it by running "Nexus Skirmisher.exe" in your Nexus folder. This tool allows you to create new skirmish-type missions for any mod you have installed. There is no new game/mission button anywhere.
There is also a Nexus Skirmisher mod bundled with the tool, which includes Nexus' default multiplayer ships ready for you to use. You run this mod like any other Nexus mod by using nexus.exe and selecting "Modifications". This mod doesn't include any missions per default and will also never display any new game/mission kind of button.
I don't have a clue what is going wrong at your end and your one-sentence descriptions sadly don't explain much. Please try to be more descriptive and give a detailed description of what you're trying to do. Also try reinstalling the Skirmisher by following the
install instructions on the download page.