I was able to accomplish this by using the Ektron.Cms.Widget.IWidgetTypeModel.FindByID()
method.
var widgetTypeModel = new Ektron.Cms.Widget.WidgetTypeModel();
Ektron.Cms.Widget.WidgetTypeData widgetTypeData = null;
widgetTypeModel.FindByControlURL("Widget.ascx", out widgetTypeData);