By reading labels carefully, you should be able to find non-dairy chocolate chips at your store.
Cocoa butter has no dairy, it is a vegetable fat: "Cocoa butter is the natural fat extracted from the cacao bean. Also known as oil of theobroma, cocoa butter is slightly yellowish in color, and while it is extracted from chocolate, it has a bland taste and only a faint chocolate smell. It is edible and is used in making white chocolate and certain confections, but has many uses beyond the kitchen."
Hydrogenated oils are trans fats: "Unlike other dietary fats, trans fats are not essential, and they do not promote good health.[1] The consumption of trans fats increases one's risk of coronary heart disease[2] by raising levels of "bad" LDL cholesterol and lowering levels of "good" HDL cholesterol.[3] Health authorities worldwide recommend that consumption of trans fat be reduced to trace amounts. Trans fats from partially hydrogenated oils are more harmful than naturally occurring oils.[4]"