Is there a recommended grit and type of sandpaper to smooth the sharp machined corners on my Ruger Flat top?  This will occasionally be carried, and I don't want to also have to carry bandages!

Paladin

Fine wet or dry sand cloth works well.
Also, stones.

Don't use a file.  The carbon steel will embed into the stainless and rust, ruining the surface.
You can however, wrap the sand cloth around a file and use it like a file to bevel edges.

If needed, after beveling the edges you can use Scotchbrite pads to restore the original grained finish.
Auto supply houses sell Scotchbrite pads in a number of grit equivalents for car painting.
Many hardware stores sell Scotchbrite type pads in steel wool equivalents.

These pads are similar to the green pot scrubbing pads sole in grocery stores.  You can even use the green pads to start.
To prevent tiny scratches were a pad is reversed, don't rub.  "Stroke" the pad in the same direction the original satin grain runs.

When working, wrap off other areas with tape or paper towel to prevent abrasive dust from getting into the action or working parts.

OP, this guy knows what he's talking about.

220 is probably a decent place to start.  Depending on how much metal I'm looking to remove, I might start as low as 100 grit.  Depending on how smoothed and polished I want it, I may go up to 2000.

Thanks guys, off to the hardware store.

Paladin

It is NOT just the carbon steel from the file.

You are exposing iron when you alter the shape of stainless.

'Passivation' (nitric acid dip mostly) is used to then remove free iron from the altered surface so it cannot rust.

The surface of passivated steel is mostly chromium.
Exposed atoms of iron have been removed.

Various diamond files and tools would get the job done without the file/steel issues.

I need to deburr the trigger on my .44 Blackhawk.  It is dangerously sharp.

Any removal of metal from SS exposes iron in the alloy.
The main material in SS (except for a very few specialized grades) is iron.

Altering the surface exposes more of the iron that is already there.

I used a ultra fine gunsmithing stone one mine. Something like this.....

https://www.zoro.com/norton-sharpening-file-rd-ao-orangebrn-med-61463686475/i/G1688023/

I did mine with some fine India stones and finished with 1500grit wet/dry over a tiny file.

Stainless can rust as soon as you remove anything unless it is passivated after removal.

We used some rather potent acids (nitric) and sulfuric) to chemically scrub the surface of iron atoms exposed by shaping the metal.

Stones are your fiend for many jobs like this.
Make sure the sure has never been used on carbon steel.

Even then an acid dip will make sure it is clean of iron.

What kind of stainless?

While some grades are slightly more resistant the main constituent in Stainless steel is still Iron.
Next is Chromium.
Then some Nickel usually.

I did not know that.   I broke the edges on my SS guide gun lever since it was breaking skin on recoil.  That was a number of years ago and no rust.  That could be a function of our extremely dry climate though.

Low humidity, few changes in RH, and some plain old oil will limit rust and corrosion on stainless.

The chlorine (chloride) in your sweat attacks most type of stainless if allowed to remain on the surface and makes a white corrosion product and pits in the metal.

When I got my Ruger Speed Six (2&3/4" and stainless steel) I did two things to it.

I removed the hammer and ground off the spur on a big grinder in the shop and then used sandpaper to finish it up so it looked smoother.  
Then I used some sandpaper, wrapped around/over my trigger finger, to take the sharp edges off the trigger/trigger guard, cylinder, etc.

Then I wiped it off with the same oily cloth I wiped off the blued and parkerized guns with.  Never any rust/pitting, ever.  Stainless or not, I wipe down my guns after use/handling with that oily cloth.   That Speed Six used to get dunked under water in the rivers at home quite often as it was my carry gun when wading the rivers to small mouth bass fish.  I'd just bring it home, disassemble it, set the oven on 200 F, lay the parts out on a cookie sheet and put it in the oven while I showered.  Get out of the shower, pull the cookie sheet/speed six parts out of the oven, let it cool, wipe the parts with the oily cloth, put it back together, squirt some tri flow lube on that moving parts, load it up and put it in my pocket to walk to work.

Now, completely different experience with my stainless steel Colt 80 series Government Model.  I brought it home, disassembled it, wiped off all the parts, lubed it up, wiped it off and put it back in the box.  About a week later I pulled it out of the box and was super pissed off.  That damned pistol was turning orange on me.  Not fingerprint/palm print type patterns, just a uniform front to back, side to side, top to bottom orange, almost as if it had been spray painted with an orange clear coat.  I'd never seen that color on any gun, let alone a damned stainless steel pistol that I'd taken the time to wipe off, lube up and never even got to shoot yet.

I sat down in the floor with some oil, the cloth and some 0000 steel wool (yeah, not stainless steel or brass wool) and went to work.  3n1 oil, 0000 steel wool and elbow grease and after awhile I had it shining again.  No trace of the orange rust (?) was left.  It never did that again.  I would not have thought it would have done that in the first place, especially after I had disassembled it and oiled it up.

Sometimes weird stuff happens.

Sounds like some parts that skipped passivation.