I rarely uninstall the drivers (never had an issue) - but, if I was going to, I'd take your second option: Remove all Nvidia drivers, including display.
Nvidia recommends Uninstalling all from Add/Remove programs because all the Downloads are included with the newest. IE: 60 series and 70 series are included. They are trying to fix some of the older glitches that occur over time.
Of course as always I create a Restore Point just in case; then remove Nvidia drivers, run CCleaner then Exe. new download . Never had any problems and I've had the Nvidia for 3 years now.