Very sorry about your sons accident.
What is scaring you? The anaesthetic? Having to "cause" another wound?
As your doctor has already said, a graft will cover the wound, reducing the chance of infection, and will reduce scarring. The problem with scars are not just cosmetic. Scarred skin can cause contractures - it becomes so tight that it restricts movement, particularly around joints, and can reduce blood flow in a limb, restricting growth and development.
Some burns patients need repeated surgery to release contractures, and have as a result very very poor cosmetic appearances, although usually a more functional limb.
The graft will be so called split skin - so they shave off a relatively small area from the donor site and put it through a meshing machine, which turns it into a sort of skin "net" that is stretchy and can cover a much bigger area. The donor site will heal well, because they only take epidermis, the top layers, not the dermis, the lower level of skin, and very quickly. It is however often quite painful immediately after the procedure, just like an area of gravel rash is. They can put on local anaesthetic soaked bandages to help. Burns units are also very good at pain management usually.
The graft site will still be scarred, but it will be much better than healing by secondary intention - the posh name for just leaving it.
Ask if you can to see pictures of before and after results by your plastic surgeon. They may reassure you about the end result.
PS am anaesthetist, not surgeon.