Don't do private cremation through a humane society...
That is kind of a broad statement to make as there are thousands of humane societies in the U.S. and they are independent of each other. Anyone can start a rescue group or shelter and tack on humane society to the name. Local humane societies are not affiliated with each other or with the Humane Society of the United States or the American Humane Society, or the ASPCA.
I could legally put up a sign in my yard and call myself TJ's Humane Society.
So as with any organization or business each one must be checked out before you deal with them on such an important matter.