I've done something similar to a surplus S&W revolver.
-Step 1 is to take everything apart, and reassemble surfaces you want blended. On your SRH, you'd probably want the trigger housing attached to the frame, but all the other pieces need to come out of the frame.
-Step 2 is to use coarser wet/dry sandpaper to take out any dings or scratches that you don't want to appear in the final finish. This can be a real pain. On the surplus gun I just decided that some were small enough not to worry about. I used 240 and 320 grit metallurgical polishing paper for this step.
-Step 3 is to blend the areas from step 2 to the finish of the rest of the gun with 600 grit paper. At this point, you can decide that you'd like a brushed finish, in which case you use Scotchbrite pads to replicate the Ruger finish. Look at the original brushing directions before you start and replicate them- they do it enough to get pretty much the ideal arrangement.
-Final step (4) is to polish with a cotton wheel and buffing compound. You can buy inexpensive kits for a hand drill on Amazon or other online retailers. A vise or bench mount is ideal for this step, since you will want to push hard enough to actually remove material.
-After finishing, the buffing compound should be removed with a solvent (isopropyl alcohol works well) from all the nooks and crannies, then you'll need to reassemble. If you decide it's not shiny enough, you get to do steps 1 & 4 again! You may also decide that having a really shiny gun is not for you, in which case you can Scotchbrite the whole thing.
