After reviewing multiple MSD sheets, it appear that the dust from machining is about as harmful as walking down a dusty country road. It is considered a benign irritant, but poses no immediate or long term health hazard other than minor irritation. The primary binders for the carbon strands or weave are vinyl esters or epoxies. Any slivers that might become embedded in your skin would be similar to a metal or wood sliver.
As with working with any process which creates dust, it is always advisable to use personal protective equipment. However, in the context of the original post, I wouldn't be too concerned.