A mini cut-off saw, widely available, has a thin 2" circular blade that is good for FG and Carbon. OK for ALU also, but dulls quickly with that.
Amazon now has a beefier 3" blade cut off saw for around $70, or twice the price of the mini, that takes both composite blades like those used on arrow saws that are 1/32" thin, or carbide tripped blades that are 1/8" thin. The carbide tipped ones have less teeth, so might do some tearing. On the other hand, the arrow saw composite blades come with a warning about shattering. That's why I always liked the 2" metal blades on the little saw, but it is on the anemic side. Maybe it's time to take another look at saws.
Also, good quality fine particle masks are not hard to find. Carbon fiber has a distinct odor when cut without using a mask - a good warning signal.