I have a correctly wired shared neutral situation where both 15 amp brkrs are feeding 2 lighting circuits--no recepticles. Each breaker is on the opposite pole. I want to move one of the lighting circuits to a generator transfer panel. As long as the breaker in the gen. Panel is on an opposite pole as the one in the main panel am I good to go? The Generator transfer switch is a Cutler Hammer 60 amp unit and the grounds and neutrals are isolated

Can you provide the model number of the transfer switch ,so we can see how it is wired internally?