ftlupton,
I applaud you, it's a great project. Been there done that. I don't see a need to find a klunker; this gun has no particular collectability that I'm aware of now that short barrels are a standard configuration. So you might as well have a still new looking gun when you finish. It won't need refinishing when done, just cold blue touchup on the muzzle. However, I'd pull the barrel, remove the warning and re-blue the barrel. If it's a very current version the warning stamping is on the bottom and won't show. But nothing looks more unprofessional than cut thru stampings. Or if you don't want to re-blue, and if the warning is on the left side, since you'll need to redrill/tap the sight and eject hsg holes anyway, pull it, adjust the shoulder and re-install the barrel turned 90 degrees so the warning is on the bottom. You save re-bluing but it's more work; lathe work. Unless you get one of Brownell's cool little barrel shoulder trimming devices. You'll need to check the barrel cylinder gap before shooting.
Another suggestion is to cut it to 4 1/8". Why? Because if you have a medium frame or large frame Ruger SA with short barrel as I do, it will be in proportion to it's big brother, which is very cool, and still meet your objective of a more 'packable' 22 Single Six.
You will lose a little travel on the ejector rod when you shorten it and not really a problem with 22 long rifles. But for the 22 WMRs, leave the ejector rod a little long so that when at rest, it's flush with the back end of the pass thru hole in the frame. From the factory the rod is about 1/8" short of that point when at rest.
If you need more reach you can cut a little off of the cylinder pin. For maximum reach cut a notch in the ejector housing even with the end of the cylinder pin so you can swivel the ejector rod head to the right to clear the pin and continue travel. You'll need to trim the spring length a little as well.
One small benefit of the shorter barrel is when you pull the cylinder pin to swap cylinders in the field, the pin will be captured by the ejector rod head and you don't have to worry about dropping it. You can gain this "capture" feature with any barrel length by chucking the pin in a drill press or power drill and with a Dremel tool, grinding a small annular ring in the back end of the cylinder pin to align with the crosspin retainer button when the end of the pin is flush in the frame hole so the cylinder just clears it.
The last suggestion is forget the all too common bird'shead grip anybody can do that, and go to the Vaquero style 32 Single six "short" version grip; either stainless for pizzaz or just blue. You can even round the sharp corners on the butt if you like. They'll look much better and another advantage is that you won't have to spend money on a new set of grips if they are wood; just shorten the originals and fit them better to the grip frame all the way around. Then it will not only be more packable but be in exact proportion to itself as well as to it's big brother!