Good news, the 10-32 UNF screws are indeed the correct ones.
Using a 5/16″ length grub screw I was able to get enough torque/clamping force to sharpen my Benchmade Griptilian despite the smaller size hex key that goes inside the grub screws compared to screws with a head on them.
But I bought a selection of headed lengths as well (both countersunk and rounded head)in case I want to try them. I suspect they’ll be handy for ‘taller’ blades like kitcken knives, where there’s more length between the edge and the spine.