Can iPad/Safari Pretend to be a Different Browser to Avoid Nag Screens?
Try the Atomic Web browser, it's UI is a little shoddy and not iPad3 retina ready, but the features are great. It can change the user agent to pretend to be other browsers, download files and then save them to Dropbox, and has a full screen mode. 

You might also try Google Chrome for iOS, but I'm not sure if what User Agent that sends, I know it uses Webkit for rendering.