Here’s a very simply plugin which exports your nav menu’s without needing to export all your content.
By default, the WordPress export tool doesn’t enable you to export your nav menu’s without selecting all content to export including all posts and pages.
This maybe inconvenient for you if you have a large amount of content which is why Joe Hoyle & Human Made have developed a small plugin named Menu Exporter which enables you to only export your navigation menu’s.
Here’s the default export screen
After installing the Menu Exporter plugin, here’s the new option which is added to the export screen.
That’s all there is to it.
I know the plugin hasn’t been updated in more than 2 years probably because it doesn’t need to be. I did test it locally and it worked perfectly for me creating a new XML file which contains the menu’s.