Run 'real VNC Viewer' in full screen mode
VNC viewer has it's own 'full screen' mode.

To access it, move your mouse to the top of the window (where the arrow is pointing) and click the full screen icon.

The only issue with this is you cannot view multiple desktops (using the trackpad gestures) without closing full screen mode.

To toggle full screen mode quickly you can press F8 (fn+play/pause) then when the menu pops up press F