I am not sure if this answers your question because you asked about curing time. My sugar scrub is sort of a paste. I didn't need to cure it.
I found my recipe for a Sugar Scrub online. I do not have the link at the moment. It had an odd name i.e., Sugar Scrub because it also called for salt.
The ingredients are: While Sugar, Brown Sugar (I used raw cane sugar), Epsom Salt, Sea Salt, Olive Oil, Vegetable Glycerine, Vitamin E, and an E.O., F.O. or your choice.
I presume the Vitamin E helps preserve it.
I'm sorry if this doesn't answer your question.
Regards