I also perform circumcisions on non-Jewish babies both in the child's home and in my former medical office on Capitol Hill in Washington, DC.  No ceremony accompanies non-religious circumcisions. So as not to have the appearance of a brit milah, non-religious circumcisions are not performed on the eighth day of the child's life, but can be scheduled any time between the second day and the eighth week of the boy's life, the earlier the better.  Even if the boy is to be raised other than as a Jew, if the birth parent is Jewish, I will conduct brit milah on the baby and will not perform a non-religious circumcision.