A needle file is the right tool for the finishing strokes
They come in all shapes one of them is with no tooth on the side,,
The procedure for DIY using hand tools I use is:
Measure twice and cut once,,, Calipers and your eye and a sharp distinct cutting line and angle,,,
First use a hack saw if needed to remove big pieces,,, fine tooth blade for thin items tpi 24 or 32 - bimetal ones are now not so expensive,,,
Then use a quick running small power tool like Dremel the Greman Proxxon makes some amazing ones as well, I have both and the expensive proxxon is a better tool,,,
The trick is to use your eye no and with the Needle file get closer and closer to the line, when ever the little teeth gets filled up you turn the file on the side and tap it gently on the vise to whip off the tiny metal flakes so they don't scratch the surface your working on, switch angle 90 degrees from time to time ,,,
Now cleaning, water and soap before drying - don't remember to clean your hands as well,,,
Now test fitting can begin again use your eye,,,
Then continue, file, clean, test, file, clean, test and have fun!