I don't use an iMac but Safari on the iPhone does have a Private "button" when you press the two squares in the bottom right to look at your open pages or add a new one. I assume this is the same functionality (no history, cookies, etc.) that is on the iMac.
Sorry if this is a separate post. I upgraded to IE 11 on Windows 7 and now I can't edit my replies. Hopefully it's soon enough that the board will combine my posts.