You can use javascript and a HTML item to resize a Cognos Report Studio control.
For example, if you wanted to resize a Select & Search prompt control then you can add a HTML Item to the Report Studio prompt page and then add the following javascript:
<script>
el = document.forms["formWarpRequest"].elements["_sws_<parameter name>_selectChoices<prompt name>"];
el.style.width=500;
</script>
Note that you must name the form element based on the parameter name and the control name that you defined in the Report Studio properties panel.