You can modify the webpart. Just change GetString("general.search"
to ""
and it won't use search when the webpart doesn't have a value.
public string SearchButtonText
{
get
{
return DataHelper.GetNotEmpty(GetValue("SearchButtonText"), GetString("general.search"));
}
set
{
SetValue("SearchButtonText", value);
btnSearch.Text = value;
}
}