It's quite a strange logic. Bathing too early in the morning baby might catch a cold. And it's best to let the baby become more awake before showering. It's just like for us adults when we shower too early, we also feel colder in the shower, easier to catch a cold if not careful.
Mucus is sticky and yellow coz his body is trying expel all the bacteria/virus. But to some folks, they say yellow mucus is heaty whereas green mucus is cooling.
I know some mothers in the forum feed more water or feed barley water. Maybe you can ask your mother in law to cook barley water (without sugar or winter melon) for your baby?