Avodah Zarah 27 - Performing a Risky Operation
An Israelite may circumcise an idol-worshipper if the latter wishes to convert, but not to remove a parasite from under his foreskin, which, as any cure, is not allowed - unless refusing to do so will cause animosity.
Whether a pagan doctor may circumcise an Israelite is the subject of a disagreement. Rabbi Meir forbids it, because of suspicion of murder or mutilation. Rabbi Yehudah bar Ilai allows it, because of "you will surely circumcise" but does not approve of it. Rabbi Yehudah the Prince forbids it and allows only one who is obligated in circumcision to circumcise others, based on "and you (Abraham), keep the covenant."
Most of the laws about idol-worshippers are not practically applicable today, but the following discussion is. When one will surely die if left untreated, he can go to a pagan doctor, who may cure him, even though there is a suspicion of murder. In general, one is allowed to make a risky operation, which may have a chance of success, even though by doing so, he may shorten the patient's life. This is derived from the behavior of four lepers during a famine , who decided to submit to the enemy who might have killed them, but who might also let them live.
Art: Francisco De Goya y Lucientes - Self-Portrait with Doctor Arrieta