As the question was posed, I assume the aircraft has just departed, hence the en route tracking is irrelevant. In situations like this the instruction is usually for separation, possibly against a go-around most of which have standard actions and usually include a heading to fly. Therefore giving a heading to the departing aircraft will assure the separation. It doesn't matter if there's a strong cross wind both aircraft will be subjected to it. One aircraft on a track and one on a heading doesn't ensure anything.