Yes sawdust is fine as a surface mulch, because when it is on the surface it does not rake nitrogen from the soil to break down.
Whether you need it on your paths is another matter. I would use whatever is most available, even compost if you have enough. Unless your paths are currently full of weeds, in which case a layer of cardboard with some sawdust on top is an excellent weed-suppressing mulch.
I’ve been using green waste compost on my paths, but only because a bought 100 tons of it for the cheap price of £1,000. I hope that it will create strong soil covered with grass and clover, that is able to take regular traffic. Only time will tell.
I also used some straw and that seems great for paths, also good around perennials and trees.