This feature is probably something that should be in core and the change is that a client already asked you for this feature. There are a lot of plugins on WordPress.org that do this and much more but this solution is clean since it still uses the WordPress widget. It only adds a selectbox to the settings screen.
So when a client ask for it in an existing project it still knows where the widget is and a new selectbox doesn’t make it confusing for your client.
https://gist.github.com/markoheijnen/2572299