It looks like they’re veneered. The way I’d go about it would be giving them a sand/removing the remaining veneer and then either paint them or apply new veneer.

Yeah your dad is right, but using a slightly bigger screw (I’m assuming the box is made out of plastic) or tapping a bigger hole might be a better idea. Alternatively you could ask your dad to help you replace the box, it’s not the hardest thing in the world and it’s a nice skill to have!