Would a small hole in a Faraday cage drastically reduce its effectiveness at blocking interference?
It's fairly common to make Faraday cages out of mesh rather than sheet copper, so you can imagine that a single small round hole is not going to degrade the effectiveness enormously. But the holes in the mesh must be much smaller than the wavelength you're trying to screen. 

In particular, it's the largest dimension of the hole, not its area, that matters. A 1-mm round hole will allow much less leakage than a seam 10 mm long but only 1 um wide.