Every proof I've seen of Snell's law from Fermat's principle uses some sort of variational argument, mostly involving variational calculus. Niven's wonderful book, Maxima and Minima Without Calculus has a geometric derivation, but also has to rely on a variational argument (e.g. one that treats the point of refraction R in a broken line segment PR+RQ, representing a luminal trajectory, as a perimeter and showing that the path's optical length is minimum iff R satisfies Snell's law).
However, is there a simple derivation that does not rely on a variational argument. I feel that there should. The transition from path length to optical length seems to be a piecewise geodesic diffeomorphism of the Euclidean plane (minus the line of refraction) such that straight lines transform to optical geodesics, which is done by some sort of scaling transformations on the half-planes (homothety about R?). Is there a derivation of Snell's law that approximately follows this line of thinking?