After much experimentation (ok, a couple of different things), I have finally found the perfect solution, for me.
My first attempt was a Rhodia Premium #12 (a little bigger than A7) note pad. (I got a batch of them for real cheap.) This worked well, but it stuck out from the edges, and I had to move the Mac back a little to get at the button.
Now, I have a stack of 3 drink coasters, about 12 mm high. They fit exactly under the flat base of the fan, and make the Mac Mini look like it is floating on air. And there is more than enough room for my finger.
Problem solved.