It is ok to use a non-muslim judge. Prophet Muhammad (pbuh) calls on muslims to respect christian judges and churches, and for no muslim to fight against their christian brother.
There are even authentically recorded incidents in which the Prophet advised some individuals not to accept Islam for a time being, due to their safety. In one instance, a person by the name of Amr bin Abasa Assulami came from a far distance to Mecca to embrace Islam. It was a time when Muslims...