I would recommend you use Linux live CD/USB drive to modify your DSM "image" partition.
There is high risk of bricking your device. You must understand what you are doing...
Steps:
1.Boot your device with Linux live media.(or SSH into your DSM)
2.Open a terminal and check your "image" partition id with the command "blkid".
3.Locate your boot and image partition,then use command "mount" to mount it.
4.(Optional) Backup whole DSM boot drive into image. "dd if=/dev/hda of=/root/synoboot.img"
5.Now you can copy your new driver extension file to the image partition.