I once had a need for permutation hashing as part of a 2D sampling algorithm. My approach was to compose the hash using only reversible steps (to ensure that it's a permutation), and then use cycle walking to reduce the domain size from a power-of-two down to an arbitrary non-power-of-two size if needed.

I published my implementation in the Pseudorandom Permutations section of my "Correlated Multi-Jittered Sampling" tech report: https://graphics.pixar.com/library/MultiJitteredSampling/pap...