For outright safety, i would recommend using the Snowdon range path up the mountain.
It has the easiest terrain anywhere on the mountain, if you are worried about the personal safety of your young son.
There are no steep gradients, and no potential slippery rocks to worry you about, and its the only route where you can climb the mountain without using your hands.
I know the Miners and Pyg tracks are amongst the most popular routes up the mountain, but for outright safety for someone using sticks, and may be scared of heights, the Snowdon Ranger path offers the best alternative for a successful attempt on the mountain.