Fn+Ctrl+F8 will highligh the Finder menu bar icons on the right, arrows will navigate you to the Keyboard preferences icon. The furthest left of the icons on the right side will get highlighted, then right arrow to the one you wnt and down arrow to open the menu and select the option you want. Note that the Option key will make different menu options available in some of the icons.
Depending on how you have your Function keys configured, the Fn is optional. Of note, Fn+Ctrl+F2 will activate the Finder menu bar's Apple icon on the left hand side.
In macOS Sierra you can also use Siri to help with this. Invoke Siri with whichever keyboard shortcut you choose from System Preferences >> Siri::Keyboard Shortcut, for example Option+Spacebar
...then say "Turn on the Keyboard Viewer"
...and voila:
Unfortunately, Siri will not close the Keyboard Viewer, nor will Command+w