Muzzle blast from a short barrel can be more distractive than recoil for young people. When you consider an 18" barrel on a bolt action rifle, touted as a light weight, you will have 6" of action. Or the equivalent
of a 24" barrel on a single shot NEF rifle.
The 24" of barrel and of course would not weigh anymore than an 18" bolt gun. Personally I don't see any reason for a single shot rifle to have a shorter than a 24" barrel. You can reduce the weight by using a plastic stock if you want.
I would get a standard length 243 and install a youth stock for the young folks, or cut off the stock and save the cut off piece for later lenghtening.
Very short rifles are whippy and not that easy to shoot. Most of the weight in a Handi is in the stock and action part. granted 4" of barrel add a few oz. The little extra forward weight will help to steady the rifle for more accuracy.