It is a general pattern. Whenever the larger evolutionary pool encounters the smaller one, the larger pool's viruses spread like wildfire through the smaller population, wrecking it. And it's not just viruses. Whenever predators from Eurasia/Africa, the "Old World", the largest landmass, arrive on an island, it is an extinction event. How much destruction has the housecat wrought?
Now, perhaps this is, fundamentally, an unstable dynamic, literally in the dynamical-systems sense, and the situation cannot be maintained. Ultimately they will come into contact with these diseases; the only question is how and when.
(To strike a philosophical note, however, your death is also inevitable, yet you seek to delay it.)
So perhaps some protocol, as you suggest, of extremely careful, "clean room" contact, with vaccines, or something like that, might be possible and desirable. How to win sufficient trust, I don't know.
But the disease aspect is important.