First of all, I would like to mention that the passing on of the dragon's powers isn't such a simple matter in the first place. I might be wrong but judging from the different dragons' back stories, it is pretty much evident that the passing on of the dragons' powers is not supposed to be genetic. A genetic transfer of powers would mean that a dragon would have to marry someone and bear a child which doesn't seem to be the case in any of the dragons' stories.
Take Shin Ah for instance. His back story revealed that he lived and was trained by a previous Seiryuu who wasn't his father. None of the dragons' back stories gives any sort of hints that might suggest that the dragon's powers only appear in his own lineage. So that proves that the powers aren't transferred genetically. It is more like "magical".
It is shown that when a dragon is grows old, the powers are slowly magically transferred to a younger person who then carries on the previous dragon's will. However, there might be other reasons for a dragon to lose their power which are not so clear yet.
Now as for Zeno, from the information that the Manga has revealed so far, Zeno is immortal and it is not possible for him to transfer his powers. In fact, it is not up to a dragon at all to transfer his own power. It is simply not a matter under his own control. None of the dragons can simply decide for themselves to transfer their power to someone and it is definitely not genetic.
So I would say, that Zeno cannot transfer his power to someone else. And since he is immortal and doesn't grow old, his powers don't need to be transferred to anyone else. His body is simply always good enough to wield the power of the dragon.
There might be another bigger reason behind Zeno's immortality than simply being King Hiryuu's shield. I think it is Zeno's responsibility to unite the four dragons. They might sway from their beliefs or true responsibilities. But it might just be that Zeno was the one destined to always bring together the four dragons. He is the only dragon alive who had actually met King Hiryuu. It might be his responsibility to overlook the new King Hiryuu and guide him and the other three dragons.