Do you want to remove the CellChangeTimes information? Or do you want to save a copy of the notebook with the CellChangeTImes information removed but with the original notebook retaining the information?
In the first case you can execute the following in the notebook and then save the notebook:
Module[{nb},
nb = EvaluationNotebook[];
SelectionMove[nb, All, Notebook];
SetOptions[NotebookSelection[nb], CellChangeTimes -> {}];
]
In the second case you can do this with a copy of the notebook. Or you can get more sophisticated and create a temporary version of the notebook in which the CellChangeTimes are removed and which is then saved, leaving the original notebook untouched.