You can work it with your thumb and see how it cleans up as some folks like to use their thumb over fine grit wet sandpaper to polish a crown, and it seems to work.
Personally, I like to cut a 60° chamfer with a lathe, then polish. Belts and suspenders approach proven to work. Without or without a lathe, I would have used the ball bearing process I have posted about here a number of times.
Using a series of ball bearings (guess you could use glass balls or marbles), from about one and half times the bore diameter, to right around bore diameter, and using sandpaper of different grits from 120/180 up to 320 or finer (I take it up to 1000 grit
if I want a mirror finish, think working on someone else's gun). A couple of turns of the muzzle over each ball bearing with progressively finer sandpaper over them gives a smooth barrel crown to bore transition.
Basic idea is to hold the sandpaper over the ball bearing (you can place ball on the floor and hold paper with your feet, maybe on a pad or thin carpet if you don’t have a lathe to chuck up the barrel in) and rotate the barrel bore on the bearing with the sandpaper on it. Easy to keep barrel square with the floor. I’ll start with the larger diameter bearing and roughest grit paper and end with a smaller ball bearing near bore diameter, repeating with progressively finer grit sandpaper. I stop when I have a slight chamfer on bore and rifling lands that is highly polished.
I use Dykem (or a Sharpie) to mark the inside the bore so I can easily see when I starting to clean up everything without going too far. Note the 60° chamfer in the photograph was cut on a lathe, I just use the ball bearings to break up the lumps and sharp edges and polish the crown.
Note that with any method involving sandpaper, and your barrel is already finished, you are going to remove finish from the face of the bore if you don’t protect it. I’ve used ‘masking’ tape with a hole punched through it (use a wad punch), but only on other people’s gun’s, not worrying about the finish on mine.