Appear Offline in Skype for Business (Oct-2017 Update)
You probably have the need, from time to time, to remain connected with your Skype for Biz client but go into stealth mode. "Appear Away" doesn't quite get the job done. Like the Lync client before it, the SFB client can be configured to provide the "Appear Offline" option in the "My Status" menu:
Note that the option is available only after signing in. If you first cancel your login attempt, then open the "Sign in as" menu, "Appear Offline" isn't there.
You may notice that the option is available from the Skype for Business icon in the system tray. When you try this, Skype signs you in initially as being offline but resets your status in the blink of an eye.
AND FINALLY HERE'S HOW TO MAKE ALL THIS POSSIBLE
You'll need permissions to edit the registry. For the 2016 version, here's the DWORD you need to make:
The entire "Office" key was absent from my new Windows 10 machine, after having installed the Office 2016 apps from the Office 365 installer page. So you may need to create the "Office\16.0\Lync" series of keys yourself, then add the "EnableAppearOffline" DWORD.
The "16.0" path won't work on your machine if you're using Skype for Business 2013. If you're still using that version, substitute "15.0" in the key above. The DWORD, its value, and the rest of the registry path would be the same.