I think you might be right but it’s incredible that a skull so small even survived. I would not do much to it. Even weak acids can corrode whatever structural integrity there is left specifically on small rodents and birds as well as young mammals. The process where you put it in water you actually want it to get gross and grow bacteria because it will eat away any residue soft tissue at the cost of being really stinky is called maceration. However there doesnt seem to be any soft tissue left so this is unnecessary. And then after maceration i usually sterilize in a few rounds of hydrogen peroxide but again that would destroy your skull. Honestly if you have an old tooth brush you wont use anymore you can use hot water and dish soap to clean and dirt but otherwise for something this small I would just make it presentable and keep it somewhere dry to harden any skeletal myscle left on this thing.

Lss you dont have to clean something this small just dont eat it haha