The piece of 'advice' regarding wearing a face mask is the most dangerous. A face mask doesn't get rid of the carbon dust. Because what happens to the carbon dust? Some of it falls and some of it remains in the air. What are you gonna do? Leave it lying around for mummy to pick up?
The 'best practice' method of protecting oneself from airborne particulates generated by sawing carbon is to set a vacuum cleaner nozzle up very close to the workpiece to remove dust as it's generated. Wear a mask as well if you like but if you set it up carefully there should be no escape of dust.
Hacksaw blade TPI (teeth per inch). Hacksaw blades are designed to be scaled to the depth of the material being worked on. The golden rule is that should be no fewer than three teeth on the workpiece at all times when cutting. So, obviously, the thinner the material /the finer the blade /the higher the TPI. Softer materials like carbon and aluniman are thicker than steel and titanium. So, although you can cut them with a coarse blade if you desire a precision cut it's worth using a fine blade.
Hope that helps.
Oh well...here we go.
Firstly, lot's of people have a bit's box, I've got an old ally stem hanging around in it that I don't trust anymore which I think was about a quid at a cycle jumble and I am sure it's not a stretch that other cyclists have them as well, cheap steel ones are even easier to get hold of.
Hacksaws - the OP not being a complete gibbon I am sure he would not have tried to use anything too coarse so I didn't lecture him on TPI, cut carbon with something too coarse and it will drag at the fibres and burr the edges.
Emery paper is emery paper, also known as J-cloth or wet and dry depending if it comes on a thin roll or in sheets, it doesn't come in coarse grits, you are thinking of aluminium oxide paper which is not the same thing so learn your abrasives before you comment.
Needle files - you obviously dont know what one is, needle files are fine grade and small for finishing work, they come in small wallet sets. If it was coarse and thin it would be a saw file which is not the same thing at all, if I had suggested using a great big round file with cross hatching like a car tyre tread then you might have had a point.
Carbon dust - as it's just one job and there is not enough present to persist in a dangerous manner than masking up and working outside will be fine, a hoover is not the same thing as a proper workshop extractor, the filters are not rated the same way and neither are the bagging arangements so just using a hoover would be no better than not using one.
I sell tools, if you want to keep being rude I can go at this all day.
So why don't you just relax and help yourself to some more WD40.