I am researcher in area of electromagnetic eavesdropping. Especially I am interested in graphic lines as sources of valuable emissions. In this place I would want to began discussion about electromagnetic safety e.g. laser printers, VGA standard, DVI standard, DisplayPort. Are these technologies safe or not? A lot of people think e.g. DVI standard is safer than VGA standard. Also we can hear DP is fully safe.
Given the OP is describing digital and analog video communications interfaces, presumably the laser printer question also refers to the interface, but that's unclear. A user should never be inside a laser printer far enough that laser exposure should be an issue, so that doesn't appear to apply.
The choice of digital or analog video signals on a shielded cable are also non-issues as far as any safety consideration, although signals may be strong enough to cause interference. More often, however, especially in the case of analog or high speed digital on long runs (e.g. HDMI) the problem of a poorly shielded/isolated cable is actually the other way in that it's susceptible to interference.
However, referring to the first two lines where the OP mentions electronic eavesdropping and "scan lines" this has nothing to do with safety at all. It also primarily dates back to CRT displays and something referred to as TEMPEST in defense circles, where it was discovered that with a sensitive enough antenna and receiver, it was possible to remotely duplicate the output of a CRT on another display. Obviously that would be a big concern for the defense industry. With the move to digital displays, the scan line emission issue is greatly reduced, although the display panel itself is still much more difficult to shield than the signal cables feeding it. And with modern HDMI signals the use of HDCP should make it much more difficult to decode any received communication signal.
Back to the safety issue for a moment, one of the other long standing pseudo-science discussions around CRTs was about ELF (extremely low frequency) exposure from the flyback transformer and guide coils. No one has ever offered any definitive proof that this is a health issue, and the physics says it's unlikely, but that hasn't prevented plenty of paranoia about ELF. Note too that this is not the same as the old "Don't sit too close to your TV." much of the older generation like myself heard growing up. Leaving out eye strain, I wouldn't dismiss the potential of a small amount of X-ray exposure from those old CRTs when high energy electrons hit the metal shadow screen. The electrons probably were never high enough energy, and the metal of the screen probably not suitable for X-ray production, but it was at least the same mechanism used in an X-ray tube!
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