Using a computer without having a mouse is a difficult task. If you're looking for a mouse for your child, this one could work very well.
Conrad Electronic
SpeedLink Axon Silent Ergonomic mouse USB Optical Black 5 Buttons 2400 dpi Ergonomic
OnBuy
Speedlink Axon Silent Optical USB Ergonomic PC Mouse - Black (SL-610009-RRBK)