Thanks for all the advice guys. I did it this afternoon and it went very well. What I did was to screw a piece of timber board inside the case (after emptying out all the computer components of course!). I then drew around a disused CD with a thin marker, as a template (a CD is exactly 12cm in diameter)
As you can see from the photos on page 1, that area of the case is mostly drilled with lots of holes. So, I drilled holes just inside my line on the bits where no pre-existing holes were.
I then used a Dremel with a cutting disc (well, 4 cutting discs, they tend to wear down quickly!). This got rid of most of the metal. I then used a grinding disc on the Dremel to get rid of the excess and the burrs.
When the hole was pretty much perfect, I used fine sandpaper to smooth out the edges and the tiny burrs left by the grinding disc. I then shook out all the swarf etc, and used a damp cloth to remove all the dust and the finer particles. Compressed air would have been good, but was unavailable.
The hole looked really nice, but I wanted it even better. So, I took an old length of thin black coaxial cable, slit it along it's length and used the outer insulation as edging. Looks like it has always been that way now.
As I had thought, the result is that the fan is running a lot quieter now. I have it spinning very slowly (at 5V), but the cooling effect is still excellent. Yes folks, a working PC with just one fan in the whole caboodle. I can barely hear the PC, the high-pitched noise from my router is now deafening! If only I could move that now
I have a program running so I can keep an eye on temperature, but it is fine.
