SRS is correct that the Zuni do not spell the name with the tilde. It is used on the title and in all of the introductory material to the book as published by The University of Arizona Press. When I lived in New Mexico, I do not remember seeing the ñ but on a recent visit I saw it placed on their work by some artists. They may have copied it from recent books and tourist material, thinking the pale people know best.
When I visited Zuni two years ago, I saw Cushing's book in the home of one artist I visited. He said a number of the tales were still told.
Most southwestern puebloans took delight in misleading investigators into their culture and religion, but among those that I have known, there is a willingness to share tales like those taken down by Cushing. Incidentally, Cushing was not a well man, and needed care by the Zuni. He was taken into one of the clans, and participated in some religious rites. He was only some 40 years old when he died.

My objection to much of the native story-telling done by us is that it is influenced strongly by our own beliefs. Those interested in the cultures of these peoples should look beyond the current homogenation of beliefs, dances and dress among peoples of strongly different original cultures as seen at many modern "pow-wows."