I'll warn you to start with that a lot of people have reported problems with the 560 drivers in Linux. However, what you want should be possible. Follow Aravisian's instructions here, but change every 555 to 560:
I did check, and nvidia-driver-560 IS 560.35.03. (to check, follow the instructions above far enough to add the PPA, then sudo apt update and apt list nvidia-driver-560.