Control+F7 (or System Preferences > Keyboard Shortcuts > Full Keyboard Access: All Controls). Then use Tab and Shift+Tab.
Also, for shutdown dialog (and other) navigation is not needed at all: Return = default button (Shut Down), Space = alternate (focused) button (Cancel).
That tip on full keyboard access is pure win. If I could up-mod this comment a dozen times, I would! Many thanks! This has pestered me for about a decade now.
Also, for shutdown dialog (and other) navigation is not needed at all: Return = default button (Shut Down), Space = alternate (focused) button (Cancel).