Is it an option to set url on baseproduct-level instead of variant level and then just select do display your desired variant in search result?
Are you using the accelerator? Then another option is to group variants in listings with _templateSettingService.SetTemplateGroupings(item.TemplateId, item.GroupingFieldId);, this can also be defined in Litium BO:
Currently there is a bug when setting this from backoffice UI, not sure if that bug is also in your version.
See also the related question Group variants on category page