Thanks everyone, it was a challenging and fun project. I don't think I'll add sights, trying to stay true to the original. Jack's theory is Beck perhaps was using up stuff in the shop and, while most guns like this would've been smooth, he had a chunk of rifle barrel on hand. Also, on the original gun, the buttcap was made from two pieces of brass soldered together, and he said it appeared to have been done not as an in-use repair, but perhaps to get a big enough piece of brass to make the cap. That's frugality!
Anyway, at coat-pocket pistol ranges, sights wouldn't be really needed I suppose. I tried 5 shots at about 5 yards, firing when the top of the barrel appeared level and pointing at the target. It hit about 6" high of my point of aim, but I think it would've been effective:
