Print out a page with a grid on it (or find something in the recycled paper as we did) for practice with the paper cutter.
Show the child how to use the cutter in steps.
A cutter like this will keep their fingers safe while providing a challenge which can be altered depending on the complexity of the paper grid provided.
Much concentration is required to line up the paper, position it straight to the blade and then to keep it in place. There is also a built-in control of error as the paper will not be cut to the grid if all of the steps are not carefully followed.