Larry,
I think that is a great idea. A number of museums have been doing this and are thinking through and dealing a variety of issues related to audio in museums including: users, environmental factors of the space, platforms, content appropriateness for listening on a mobile, et al.
You may want to look through some of the sources in our public Mobile Museums Zotero group. https://www.zotero.org/groups/mobile_museums. There are some case studies from museums (many from the Museums and the Web conference,) who created cell audio tours and who have tried other methods and platforms. We at CHNM wrote up some recommendations for museums wanting to develop mobile content in this digital white paper, Mobile for Museums: http://chnm.gmu.edu/labs/mobile-for-museums/. Cleveland State is testing a new iPhone app,Cleveland Historical, developed with Omeka in case you are interested in that at another time.
Having said all of that, you'll see that you have many options. But, first you should think about the following, because the answers to these questions will direct you in making the best choices: Is there wifi available in the building? Is there good cell phone coverage in this exhibit space? Do you know your audience, what kind of phones are they using? Do you want to update the content--add other media, edit content? Is there room, and budget for designing of signs that tell people it is ok to use their mobiles in the exhibit, or explaining how to access the mobile content--especially if QR codes are used and an QR Code reader is necessary?
Recordings saved as podcasts are cheap and easy, but would require folks to download the files before going to the exhibit (unless there is wireless and the audience uses smart phones). Most cell phone tours in museums are run through an outside vendor who manages the platform and the telephony for the project, which brings added costs.
It is good to be thinking about this now during exhibit development. And maybe after browsing through some of the articles in that bibliography, you may have some ideas about how best to use audio, or video, imagery, that can be accessible through mobiles for the exhibit and live on after the exhibit closes.