Furniture, Wood and Cabinetry Finishing - Fixing scratches and dings in cabinetry

I have alder cabinetry in my kitchen (poor choice, I know) that looks unstained and not topcoated very well. My children have made lots of scratches and dings in all the lower cabinet doors and some of the plywood panels. Short of sanding off the thin topcoat (I was told is probably lacquer) what can I do to effectively cover the marks? Is Tung oil an option? I've used the standard lemon oil (i.e. Old English) but it soaks in or dries and the marks show up again, even though they are hidden right after I apply the oil. I don't know what is compatible with lacquer or if there are really any other alternatives to sanding down to the bare wood and reapplying lacquer. I can't really do that, so any other ideas/options would be greatly appreciated

There are crayon touch up sticks available in varying colors for furniture at home centers. If you have children, then you may find just what you need to match in their crayon box.

Clean the cabinets first. Then try some paste furniture wax like Bri-Wax or Liberon Black Bison. Buff after 20 minutes. The scratches should go clear again and mostly disappear.