I've dug around and found out a few interesting things:
There does not appear currently to be a simple universal browser setting that allows the discrete removal of individual control buttons - all or nothing. Otherwise You have to roll your own.
However, if You create an iFrame and do not include the "allowfullscreen" in the iFrame tag - voilà no full screen. Please see this link for more.
Next - there are developments on the horizon - mainly about a subtree of DOM elements called the "Shadow DOM". Currently only Chrome & Opera support scripting the CSS of this feature. Safari & Firefox have it under development... please click here for a full list of browser support.
This subject of Shadow DOM discussed pretty thoroughly at CSS Tricks.