Dangers of ESD wrist wrap / mat / ground Plug Adapter in an Apartment building?
Yes, you are potentially in danger whenever your body is connected through a low impedance path to earth ground.

They key point is low impedance. You should check that your wrist strap includes an high value resistor (1 Mohm, typically). 

There are models which don't include that resistor: they are made to be used in environments where the high impedance is provided by another part of the grounding system, and they are not to be connected directly to earth ground wires.

See this other thread (@AlmostDone has posted it as a comment, but it is better to include the reference in this answer, so that it doesn't get lost).

In particular see my answer in that thread and browse the references I made there.