There are different types of DVD-RAM disks as you have found. If your new disk obviously will not fit in your drive you can take the disk out of the case to use it. I am not familiar with your exact kit.
In my 'floppy' DVD-RAMs there is a little plastic pin you push out then the case opens and you get out the disk which looks just like a normal CD or DVD.
As to drag and drop - what OS and/or software are you using?