Personally I would favour a solution whereby the stylesheet link is conditionally rendered via some logic in the code behind of the page which is triggered by a user selection. It's not as clean, but you could possibly achieve this by using some javascript too. Maybe along the lines of giving the stylesheet link an id:
<link id="mobilestyles" rel="stylesheet" type="text/css" media="screen and (max-device-width : 768px)" href="css/mobile.css" />
Then calling a function to disable the stylesheet from a button event handler:
jQuery
$("#mobilestyles").remove();
Plain JS
document.mobilestyles[0].disabled = true;
You could then store the user's selection as a cookie and remember this for future visits.