It is a mistake to believe that tools for children must not, or should not, be sharp, so they cannot hurt themselves. On the contrary: dull tools are more dangerous because the child cannot develop a good feel for the correct way to use the tool. Even a dull knife or saw or chisel can cause a nasty wound, and this becomes more likely if the child becomes frustrated and impatient because a cutting tool does not cut, and so uses too much force or loses his concentration. Far better to teach careful, deliberate work habits using tools that work as they should.
All this means that one must think carefully about when children should be taught to use the different kinds of tools. A sharp tool in the hands of a child is always dangerous. Give tools appropriate to the age, but first and foremost, the maturity of the child. One child may well be patient and mature enough to use a carving knife or saw, but another of the same age may not be. This is a bad thing to be overly ambitious or optimistic about. Every child develops at a different rate. So we cannot give good advice about what tools are suitable for children at a certain age. This must be left up to you.
It is also a bad idea to buy cheap tools, like those often marketed in "children's tool kits." Bad tools, that break or bend or go dull quickly, are at least as frustrating for children as they are for adults. This makes it very hard to have fun using them, can turn children off working with their hands, and as mentioned above, frustration and too much force can be dangerous. The joy of developing hand skills can be killed from the outset: the opposite to the effect one is normally looking for. This does not mean that one must go out and spend a lot of money. It takes time to learn to use tools, and a few good quality tools will produce better work and more satisfaction, and can cost less, than an elaborate set of cheap ones. Less is very often more in this case.