It should go well.
On a gun that hasn't been damaged by rust and pitting you won't have to spend excessive amounts of time working a surface to get rid of the flaw so you wont risk enlarging radii or washing out screw/pin holes or diminishing engravings or letterings.
There is a preferable emory cloth but I don't recall exactly which is which. Do a search its been a while.
Remember to remove all signs of a previous grit before advancing because the next grit will not.
If your working 600 having advanced from 400 don't go to 800 until all signs of 400 have been removed. Even the slightest scratch of 400 will remain if not caught with the 600 if you advance to 800 too soon. You'll discover in your practice piece if you experiment a little.
When slow rust bluing I generally stopped the prep at a uniform 400/600 for a good bite by the acids. Too fine a finish gets risky.
I know my hens are good Republicans, they cackle after they lay their egg. I do have a young pullet that leans a little left. I can tell because of her cackling before she lays her egg.
That will change after a good "roostering".