As a United States Naval medical officer, my oath is to protect and defend the United States of America against all enemies, both foreign and domestic, and not an oath to "Apollo Physician and Asclepius and Hygieia and Panaceia and all the gods and goddesses".
The Hippocratic Oath is an outdated classical relic that, if followed, would prohibit surgery.
"I will not use the knife, not even on sufferers from stone, but will withdraw in favor of such men as are engaged in this work."
In any case, however, the Hippocratic Oath has no prohibition on the waging of war.