Tommy,
If the original rifle was CC Hardened then you should have it annealed first. Not a thing you can do easily at home. Once that has been done, then you can repair any dings or burrs etc, then, and only then resort to fine abrasive paper backed by a hard surface. Many people use files for this, but I prefer to use a wood or hard plastic strip of the same width of the tape. Should your abrasive come in sheets it may tear easily readily into strips, if not an old 'Exacto' blade will cut it easily.
Starting off with something like 200 grit paper then work down to 400 or even 600, anything finer is not really needed. Polish lengthways and do not do one part one way and another part in a different direction
When polishing, use new sheet lead jaws for the vice holding the work and be sure to wipe any dust off the whole action and the jaws when moving the parts, you don't want to make new scratches on them.
Do all the curves first, and then the flat surfaces. As Quarter-bore says, stay well away from buffing wheels and machines. Hand polishing is the only way to go.
If your not sure you are capable of the work, have the smith who will be doing the CC Hardening do it for you, he will charge of course, but he should have the necessary skill and experience to do a good job.
Just my 2 dollars worth. 2 cents doesn't buy you anything these days.
Harry