[Phlogiston]

That is good. Then you should replace all of the plywood on which that layer of veneer is applied (as opposed to replacing just the top layer of decorative veneer). It is likely that most of the layers of the plywood are split.

Doing a touch up is not wrong. Just saying, if you are like me, you will look at that spot every time you walk by. And when the crack shows up again - - you will be annoyed.