I can't think of any logical reason for why hay wouldn't be safe. If they eat it it wouldn't be a problem; it's just dried grass (I mean, depending on what type you choose but generally speaking, it's just grass). High-quality hay should be virtually dust free. The only real 'risk' would be hay-pokes. And even if you use a very soft hay (i.e meadow hay) there would still be some degree of risk attached.
That same risk is attached across every species who are offered hay; most notably rabbits and guinea-pigs, where hay is a vital component of their diet. It's not life threatening, and if it were to happen, it's very easy to treat and is of (generally) really no major concern at all.
Timothy hay and alfalfa legume hay are more pokey, and IMO best avoided (I dont even use either with my rabbits, nor guinea pigs). But a high quality meadow hay should be nice and soft, and although the risk of hay poke is always there, it's a very, very minor risk that wouldn't deter me (personally) from using it. But it's up to you.