A Select List (with height set to 10) to start with...
It is not possible to apply a scroll bar to a select list control.
If you really must, you can wrap the select list in a fixed-sized container and apply a scroll bar to that. In my opinion the results are hideous and totally unusable...
Create the container using the Element properties for the select list item:
Pre Element Text
<div style="width: 20em; overflow-x: scroll; overflow-y: hidden;">
Post Element Text
My recommendation would be to rethink the presentation completely.
but would be nice to see this also on each side of a shuttle box.
The DIV container would have to be applied to shuttle lists using a dynamic action.