The religious seem to think they have some sort of monopoly on ethics, but in fact ethical and moral systems long predate religion, and can be found in many higher animal societies. A course in ethics would be easily taught without endorsing a religious view.
Comparative religious ethics could be covered as long as no one religious ethical system was endorsed, focused on, or promoted as "right".
Ethics as a philosophical examination of various forms of ethical belief can be done in a relatively secular way without promoting a religious or irreligious point of view. Teaching a particular set of ethical principles as true is, however, way out of the question. As long as it isn't an excuse to promote one particular set of ethical beliefs, but to examine the nature and logical foundation of various ethical systems, this should be fine.
While religion implies a code of ethics the reverse is not the case. Ethics is a code of conduct, a set of moral values, and accepted right and wrongs. The question implies there can be no ethics without religion. If that was the case then ethics would only apply to religious people.
Just as any religious instruction in school must be purely descriptive to be compatible with the childs (not the parents!) religious freedom, so must ethics. Except possibly for the basic values of the system of government employed in each nation. In practice, teaching ethics will require teaching the rules of proper argument and thus enhance critical thinking, which would be opposed by religious parents since religion is based on authority rather than rational argument. They will say that it infringes on their religious freedom, but they will be wrong. Religious freedom is an individual right not a collective right of the entity called "family".
Ethics comes from more than just religion. A person can not believe in anything and still be a really ethical person. Plus there is all types of ethics, moral ethics work ethics, family ethics. It really depends on how the school teaches it and how far they go with it.