Hi Ockert you can achieve this by disabling the default scroll bar on all divs that have them enabled using css. Then the best way to implement it after is to create a widget that assigns a css class to it's parent div and then you can create a custom scroll bar out of markup and css that gets applied to the parent div with your custom class on it. This will end up being something you inject through your widget. You will however have to cater for every browser you would like to support. You can use jQuery to cater for user interaction with the scrollbar. There are various interesting ways to simulate scrolling with CSS and jQuery.
You can do this all from scratch or use something such as jScrollPane, which is easy to implement.