Pause for a moment to be a woodworking nerd: Not all "sawdust" is alike. There's an entire science behind chip formation , and in a wood shop the type, shape and size of chips varies widely depending on the cutter and operation. Wood shops produce shavings of all sizes from hand plane shavings which resemble paper tape to sanding swarf which is microscopic powder. If I were to choose from my own various production of wood chips to use as cat litter, I think I'd go for planer/jointer shavings which are confetti-like and similar to what they used to sell as rodent bedding, like the cedar chips you're warned not to use for hamsters anymore. I would also try to choose a wood that is less aromatic than a softwood, maybe something like ash, maple or oak.

Apparently those wood pellets (often manufactured as a surprisingly efficient stove fuel but other uses abound) are made first by putting wood through a hammer mill which produces a homogeneous dough-like substance, which is then extruded through a die which has the effect of plasticizing the lignin turning it into basically tree hamburger. Same chemical makeup as wood but none of the original structure. I imagine this could be made of practically any size of shavings, chips or swarf.