Can I map my My Cloud drive and transfer directly from files on USB without going through router?
It all depends if your My Cloud device features a USB port, but as I can see on the official website, these devices have Gigabit connection port that can be used to transfer the files. There is no USB support which means USB connectivity is not possible. You still have to get through router to transfer the files from the available sources.
You can check the specs on the following page: http://www.wdc.com/en/products/products.aspx?id=1140#Tab3