I was told by my high school auto shop teacher explicitly never to use powdered graphite on speedo cables.
I was told to use a light coat of white lithium grease if necessary.
People here say to use the graphite impregnated grease which is probably ok since it was likely not around when I was in high school.
When I installed a new cable on Ol' Roy a year or two ago, I put some lithium grease on my fingers and wiped the entire cable. No chunks or heavy deposits, just a light coating. So far so good.