It's possible, you can simply use jQuery to substitute the 'meta tag' that references the cache status with an event handler / button, and then refresh, easy,
$('.button').click(function() {
$.ajax({
url: "",
context: document.body,
success: function(s,x){
$('html[manifest=saveappoffline.appcache]').attr('content', '');
$(this).html(s);
}
});
});
NOTE: This solution relies on the Application Cache that is implemented as part of the HTML 5 spec. It also requires server configuration to set up the App Cache manifest. It does not describe a method by which one can clear the 'traditional' browser cache via client- or server-side code, which is nigh impossible to do.