I just noticed that there is a plugin to import/export camera's.
That is esssentially what I described but using the plugin is of course much easier.
This plugin exports the camera's to a CSV file which you can import into the second project. Be aware that it will overwrite existing camera's if they have the same name.
Disclaimer: I haven't installed this plugin and did not try it myself.
If you have the plugin "Plugin manager" installed you can see it in the list with all plugins.