If weight is the issue, most 20 ga pumps are not much heavier than a single shot.
Entirely your call but you might want to give this some consideration. I can tell you that your son will outgrow the single-20 but never the pump-20. As far as hammerless singles, they did make them and not impossible to find. These are domestic and well as foreign makes. Most if not all, are standard length models. Your ten year old should be able to handle a full length but you are a better judge of that. ....
Be Safe !!!