Hello "A Grandson",
Welcome to the forum. The Puchalski/Wawrzynski reference has a complete list of recipients which starts on page 81 of the book. If your grandfather is not listed there then it's unlikely he was awarded the Cross of Independence with Swords.
Do you have just the cross, or is there any accompanying documentation? Is it possible to have you post picures of the cross?
The 'barbell' you are referring was just a device used to mount decorations onto a uniform or other clothing. It was not a piece included with this decoration.