Rand may not need the ter'angreal. When he went through the rings and lived through the lives of his ancestorys he saw the AoL the day of the strike at SG and the Aiel were seed singing. Depending on how good his memory is he might well remember it from that vision.

Added to that one assumes that LTT might know the theory of seed singing and Rand seems to have reintegrated that side of his mind so he may be able to tap those memories a lot easier.