Even if you used batteries, is your tree sculpture really safe?
If someone gets entangled in it and the structure pierces the skin and the battery voltage is, in effect, directly connected to the person (having penetrated the outer skin layer) and that person remains entangled in the sculpture I suspect that there could be serious medical implications.
More than 99% of a body's protection against flow of current is due to the skin. A calloused, dry hand may have more than 100,000 Ω because of a thick outer layer of dead cells in the stratum corneum. The internal body resistance is about 300 Ω, being related to the wet, relatively salty tissues beneath the skin.
Information gathered from this website
I believe that before you should consider the use of an external AC power supply you should convince your self that having the tree sculpture connected to one side of the DC power is a sensible thing. I have no idea what your sculpture looks like but I'd begin by having the LEDs insulated from the metal of the tree and then start considering what sort of power supplies to use - maybe medical power supplies (that use more reliable isolation) is the way to go.
I suspect that normal "safe" power supplies do not consider that a person can be entangled in the wires.
To power a device, current has to flow thru it. That means it has to go in one place and come out another, which requires two wires.
The third wire of most outlets is a safety ground. It is not necessary to power a device, but can be useful to some devices. Any device that has a conductive outer shell is a potential safety hazard. It would only take one fault to make the shell live, like the hot wire breaking or slipping off some mounting, then touching the inside of the case instead.
In general, we try to keep users two independent faults from danger. The above example of the hot wire coming off and touching the chassis is just a single fault. Now the chassis is at lethal voltage, and you don't even know this until you touch it and something grounded. Then its too late.
In such cases, the chassis is tied to the ground line. If the fault described above happens, hot is shorted to ground, which will cause a lot of current to flow and trip the breaker.
When the outer shell of a device is made of insulating material, the user can touch it no matter what went wrong inside. Such devices don't require a ground connection, and there's often no place to connect it anyway. Usually such devices are "double insulated". That means the hot voltages are normally insulated with insulation on the wire and the like. Nothing on the hot side is supposed to rub up against the case without a deliberate layer of insulation in between. Then you still have the case if that layer fails.
Another reason for the ground connection is to allow devices to reduce both conducted and radiated emissions. Most line filters are common mode chokes, also called baluns, with capacitors to ground on the line cord side of both AC lines. The balun increases the impedance of the unwanted signals, then the capacitors shunt the signals to ground. This isn't possible without a ground connection.
Best Answer
I don't think so- I've never seen such a thing and if you look at the internal design of a typical receptacle I don't think that such a plug could be reliably backward compatible unless the insulated length was only a couple mm and the thickness very thin. Given the enormous installed base of receptacles and extension cords, such a change is unlikely to be popularly accepted.
It is possible to get even an adult-sized finger under even a normal plug, so such a design would not pass the UL 4mm baby-finger requirement if it was to be introduced today.
Here is a photo of an AC adapter plugged into a power bar receptacle. There is 120V present on the pins (verified by voltmeter) and the finger is an adult one (mine, just before my death by electrocution).
It's worse again if the pins are bent, which is pretty easy with ungrounded cord ends. Especially if some cretin pulls the plug out by yanking on the cord at an obtuse angle.