One way to do this would be by using client side js to redirect to this same chart page but with the new parameters you would like the chart displayed with.
You would want to make sure that have your chart set to take parameters from the querystring, then in your select list you would send the user to this page with the different querystring parameters that that will give them the chart they have selected.
This is not a feature of Dynamic Web Charts that is directly supported but if you can alter the querystring variables with a select list then you would get the different chart data to show.