22 short, long and long rifle rimfires all use bullets that are nominally .223" for a .222" bore - that's why the 22 Jet cartridges uses .222" bullets, so the S&W Model 53 could be very accurate whether shooting 22 Jet jacketed bullets or using the inserts or a second cylinder to shoot 22 LR with the soft swaged lead bullet.
22 WMR does use a .224" bullet that have a very thin or plated jacket for a .224" bore - which is why S&W refused to make a second cylinder in 22 WMR for the 22 LR guns (Model 17, 34, 43, 63 etc), but used to make a second 22LR cylinder for the 22WMR guns (Model 48, 51, 651 etc).
Look in Cartridges of the World or other reference book that gives the dimensions of the rimfire cartridges, it's kind of amazing how many 22 rimfires there are and how the bullets change diameter from .222 through .223 to .224 - and my copy doesn't even list the 22 S&W. It's a 22 long rimfire clone that was only loaded with smokeless powder around the turn of the century for the very small M-frame 22 ladysmith 7 shot revolver. Everything about this revolver as so small that S&W didn't want black powder loads (that were still available in 22 long) used in it because the revolver's clearances couldn't handle the fouling produced.
A 1959 Ruger Single Six would not be a convertable model, and Ruger won't fit a second 22 WMR cylinder to one either. That's not to say that you could get a second 22 WMR cylinder off ebay etc that might just drop into your gun and start shooting 22 WMR, or re-chamber your existing 22 LR cylinder to 22 WMR. The forcing cone will accept a .224" bullet and swage it down to fit the barrel with no problems if everything lines up well; if the chamber is a little of center to the bore you'll get spitting out of the barrel/cylinder gap.
