I would not go any shorter than 18". Personally I like the 22" barrel. The gun is still not very long and I can carry it straight down and not touch the ground. Maybe a shorter person could not do that and like Larry has stated, having the barrel next to my ear is not appealing to me. I have a 17" (actually it is a 14" with an unremovable 3" aluminum muzzle brake to make it 17") 44 mag barrel on a Contender and I do not carry it on a sling - straight down. Being that short does make it nice in a tree blind. Good Shooting and Good Luck.
Essentially I agree with the thoughts expressed here. Regardless of whether the .357 Mag or Maxi's are pistol rounds, on a Handi or Contender or Encore I wouldn't want a barrel shorter than 20-21 inches, and being already 22inches probably wouldn't ever touch it! Unless I needed the crown cleaned up after an accident or whatever imagined unforeseen event.
If you were using it yourself - esp on a side-folding stock, cutting it to 16+ inches might make sense.
But most folks who chop their guns to 16 or so inches I think are ONLY INTERESTED IN "LOOKING" COOL.
As for your boy, part of shooting and learning to hunt in my opinion is for the youngster to "step up" and use a real gun and not a "cutesie" warm and fuzzy toy!
Was I equipping a beginner like you are? I'd get a wooden stock (two if necessary) and shape, shorten or whatever was necessary to provide that youngster or small adult with a rifle that "fit."
Also, barrel length again - I've always believed the perfect length (if determined in a ballistics laboratory) for a .357 Maxi would be between 19 and 21 inches - to get maximum velocity from a 200-220 grain boolit. A 180grainer? Maybe a tad bit shorter, IMHO.