It looks like you've got scrollOverflow: true and you've included the jquery.slimscroll.min.js so it should work.
However, I noticed you are loading jquery.slimscroll.min.js before loading jQuery.
Try loading the jquery.slimscroll.min.js just before the jquery.fullPage.js but after jquery.min.js since the plugin requires jQuery so something like this:
<!-- jQuery and jQuery UI -->
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
<script src="http://ajax.googleapis.com/ajax/libs/jqueryui/1.9.1/jquery-ui.min.js"></script>
<!-- Plugins -->
<script type="text/javascript" src="squelettes/vendors/jquery.slimscroll.min.js"></script>
<script type="text/javascript" src="squelettes/js/jquery.fullPage.js"></script>