Step 4: Make Holes
Mark your fan's outer limits on the top of the lid with marker or pencil. This helps reposition the fan when it moves.
Then poke your pen through the blades and try to draw the limits of the inside. You should end up with a circle, likely with four chords cut off the sides.
Finally, mark through the four mounting holes so you know where to put the screw holes. Then put the main body of the switch out of dust's way.
Drill a pilot hole not hard on the line, big enough for your jigsaw blade. Then using scraps of timber for support, carefully saw your line off - that is, cut off the line you drew. This will allow enough room for air but without being too wide.
Clean up the edges of the hole using files and steel. You could also use a laser cutter, but anyone with that kind of kit could just buy a silent switch.
Ideally the cut edge should be rounded and have no protrusions - any irregularities mess with airflow and also catch dust.
Once the main hole is done, test fit and check the screw holes, and drill large enough for your mounting screws or bolts.
I chose to put a coat of spray on galvanising paint on the raw edges. This will help keep the steel from getting rusty over time.