Heatsinks, Pibow and the Raspberry Pi Zero W

Is it possible to attach a heat-sink to the Raspberry Pi Zero W whilst it is within a Pibow Zero W case? I can’t tell from the picture whether there is enough clearance as is, or that it would only fit when the clear acrylic layer is removed.

The heat-sink in particular I was using as a reference is here, however I have no idea if it fits the Raspberry Pi Zero W.

I have the 6mm one on my Pi Zero and it will not fit in the PIBOW case. Not without leaving the top layer off. Or cutting a hole in the top layer.