It is going to ultimately depend on the kid. Three years ago, I bought my kids each a Sportster. My son got a Youth, my daughter got a Full sized. My son just turned 12, my daughter will be 17 next month. I have no doubt, sometime this summer both Sportsters will wear adult stocks, and both kids will be shooting one of my centerfires (30/30 or 357max) with an adult stock.
Since you say yours are small statured, the youth might be the way to go. Recoil, as you know, is something that can be very subjective, and my personal thought is that 7-08 recoil won't be unmanageable for most enthusiastic shooter type kids.
My son shot my Ruger Blackhawk (357) with normal powered 38spls right after shooting a Ruger Bearcat with .22LR. There was a definite recoil difference, but he keeps asking to shoot the Blackhawk (even though he has trouble holding it up for long). I think he likes to experience the power of the recoil from the Blackhawk. 22s are fun, but centerfires are more 'bang-for-the-buck'.
And anyway, you have a great excuse reason to buy another Handi if you go for the wood stocked youth 7-08 and you'll have Handis with both stocks so you'll know which one fits the kids better.