I think Tolkien does describe the beast as having some kind of beak, although by no means all pterosaurs had beaks. He apparently thought of it as a sort of surviving prehistoric animal, suggesting that he was thinking along pterosaur lines, although obviously anything large enough to carry a rider would have to be bigger even than a quetzalcoatlus, the largest known pterosaur (assuming that a Nazgul weighs as much as a human being). Also, his description of the beast's wing structure is completely unlike that of a pterosaur, being more like that of a bat. I suspect that Tolkien had little understanding of palaeontology and didn't know the difference.
At any rate, I did give it batlike wings and I tried to make the head more like that of a dimorphodon than anything else, which I thought a fair compromise. Though in the event it doesn't really look like that either.