The identity of godparents is determined at baptism so you cannot change the fact that, technically, a godparent is a godparent. But you can remove an unworthy godparent from his godparenting role and allow someone else to take over in that capacity. It seems to me that, as a parent, you have a responsibility to do as much.
If you do decide to do this, while baptismal records cannot be altered, you might ask that the records be notated in such a way to reflect the change in who is fulfilling the role of godparent for your child.
