Nikolaus Kriegeskorte (the father of searchlight analysis) uses the illustration on the left.
Personally, I implemented the middle version (edges and faces, not corners, 18 voxels) as a one-voxel radius searchlight in my code. Larger radii are calculated iteratively (so for a two-voxel radius, combine the one-voxel radius searchlights defined by treating all 18 surrounding voxels present in the one-voxel radius searchlight as centers). I don't think one version of defining surrounds is necessarily better than others, but we do need to specify the voxels we are including.
update 11 September: I changed the caption of the searchlight shape images for clarity.