I'm not sure we are on the same page here. I have designed offline (AC power line) regulators which were *not* galvanically isolated, and at least 4 chip vendors make wierd little parts for this. But in a wall wart?? I've never seen or heard of any such thing. No matter what the technology inside (including capacitive-only coupling, no transformer), everything I've seen has some form of true galvanic isolation. So, if you have details of "older switching power adapters that were not always isolated", and they had low voltage outputs (apples to apples), I'd love to hear them. Maybe this isn't the right forum. Private email?
About your schematics, I've thumped you several times about seeing your circuits, and you reject me at every turn. Do they really exist? Do you? What is reality?
"So, does this mean that the zapper becomes refferenced to earth ground?"
I don't think so. SELV outputs must be earth-ground referenced, but medical-rated power supply outputs do not have to be by rule, although the equipment they are in usually is. Still, if you can demonstrate that your insulation and leakage are good enough, I don't think an earth reference is mandatory. BTW, I meant to say UL601, not 544. Some late changes got lost in the editing.
In general, having "dangerous" outputs referenced to earth ground is a good thing. For example, let's say you have a true medical rated small power supply with a 9V output. If the output terminals are floating with respect to earth, then when measured with respect to earth they could be at 3000V and 3009V. The 4KV rated transformer would be happy with that, but you might not be if you're standing barefoot in the basement.
Battery power is simple, cheap, regulated, energy-limited, and eliminates a mountain of product liability issues. But there is nothing in there which equates to "better" in terms of zapper performance. Of course, the real reason for that statement is that there is ZERO valid comparison data, but now I'm getting into an area where we agree, so I'll stop.