Your demo seems to be inappropriate, I suggest you think of an app that will have also some practical use. If I understand your question correctly, the solution would be:
1) from your Activity you need to start your Extension on the SmartWatch. Here's how to do that: Sony SmartWatch - invoke app on Smart Watch when it gets an event
2) you also want to pass some arguments to your Extension, i.e. the String you mention. This can be a bit tricky; normally, you would pass that String in the Intent itself, as an extra, but here, that is not available. You need to save that information (the String) on a location that your Extension can access as well. So, if your Activity and your Extension are part of the same app, that location can be the app preferences: the Activity saves the value in the preferences, and the Extension reads it from the same preference and displays it on the SmartWatch or whatever.