Well, solving 4 adjacent corners (equivalent to 3x3x3 first-layer corners) is easy enough. After that, you can use 3x3x3 algs to orient and permute the last four corners.
I think of it as a 3x3x3 without edges. Imagine you have already solved cross, and you are now doing F2L, but without edges. Then orient the last layer, but ignore the non-existant edges. Then permute with a 3 cycle or y-perm.