Fullscreen Browser App without navbar
I do not know how to disable the navigation bar on Safari for iOS. However, applications exist for iOS that may satisfy your requirement. You may want to search the internet for terms such as "kiosk browser ipad" or a similar query.

One of these applications is called Amtel Secure Browser Kiosk. I have never personally used it, but it is free.


  Amtel provides a secure restricted browser &amp; kiosk application for iOS
  users. Browser policies can be configured such that only whitelisted
  links are made available to the end users. The application is designed
  to help IT departments at Healthcare organizations, Financial
  institutions, Education sector, Libraries, Hi-tech, Fleet management
  etc manage browser security on the iOS devices. The Administrator can
  customize the settings to stop blacklisted sites on the devices or
  allow only favorite sites on the browser. The kiosk mode is designed
  to give the users the benefits of mobile device technology with fewer
  distractions &amp; security risks. The configuration of browser settings
  is done at Amtel Mobile Device Management console - MDM.