Youth stocks obviously fit youths better, but they are lighter and kick harder than a full size.
I'd be concerned about a 10 year old with a 12 or a 20. If it's legal you might want to consider a 410 with slugs. If you can use a rifle a 357 lever action, or a 223 is also very easy for a kid to shoot.
Check out the H&R and NEF lines of single shot youth sized SGs offered by Marlin/Remington. As somebody else offered - these are generally lighter and recoil a bit "harder" - but down loading or using anemic cartridges is a good way to WOUND and not KILL cleanly.