What is a single word for the action of causing a single small item to fall out from a sheaf of papers, as by shaking?
When I started work in an office, I had to load paper into printers, and I had to unwrap and fan each stack of paper before loading it. I also tended an enveloping machine, and I had to shingle each stack of envelopes, as well as fanning the printed letters to be inserted. I agree with your reluctance about riffle, although I also don't agree that it applies to grasping a book by the spine and shaking. Merriam-Webster gives the meaning "to leaf by sliding a thumb along the edge of the leaves: riffle a stack of paper".