Well... you're ordering a chrome lined barrel, and the first thing you're wanting to do is compromise the chrome lining?
I think you need to step back and consider that your headspace is composed of the relation between the depth of the chamber, the mounting of the barrel on the receiver, then the receiver and the bolt fit-up. Before you get ahead of yourself in this project, you need headspace gages to see just how close your bolt is to closing.
If you have a chrome lined chamber/bore that is very close to allowing your bolt to close on a "go" gage, you could lap the bolt lugs onto the receiver to gain a few thousandths of headspace without touching the chrome in the front of the chamber. If you put a reamer into the chamber, it should be of the type of reamer that doesn't touch the throat. If you compromise the chrome in the throat, you might as well not have bought a chrome lined barrel.
For short-chambered Garand/M14/M1A barrels, a pull-through reamer is typically used and the bolt is allowed to close (gently) on the reamer from the rear, then you rotate the reamer using the drive rod from the muzzle. Clean the chamber/barrel, insert the go gage, check the headspace and repeat as necessary. Never turn a reamer backwards.
Chrome lined chambers typically require carbide reamers or tooling. Chrome is pretty hard - hard enough that it prevents use of HSS tooling.
Personally, I have no use for chrome lined barrels.