The difference between an ax and a knife is in the thickness of the blade. That is, it is better to make small grooves in the tree with a knife and more difficult to make large ones, but with an ax the whole situation is radically opposite. Dry wood means larger pieces will be chipped off with less effort. This means that the difference between a knife and an ax is almost eliminated. But considering that a knife is still more convenient than an ax for making a drawing (unless, of course, the drawing is more than 1m2), then the answer is with a knife.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.