Its funny you ask your question this way, because using 3 css files is exactly how the website you want to copy does it..
They use the javascript method you can see when you mouseover the link to disable the unwanted styles...
function setStylesheet(title) {
var i, cacheobj;
for(i=0; (cacheobj=document.getElementsByTagName("link")[i]); i++)
{
if(cacheobj.getAttribute("rel").indexOf("style") != -1 && cacheobj.getAttribute("title")) {
cacheobj.disabled = true;
if(cacheobj.getAttribute("title") == title)
cacheobj.disabled = false; //enable chosen style sheet
}
}
}
function chooseStyle(styletitle, days){
if (document.getElementById){
setStylesheet(styletitle);
setCookie("mysheet", styletitle, days);
}
} <link rel="stylesheet" type="text/css" href="css/style.css" />
<link rel="alternate stylesheet" type="text/css" media="screen" title="style1" href="css/style2.css" />
<link rel="alternate stylesheet" type="text/css" media="screen" title="style2" href="css/style3.css" />