Earth and mains decoupled power supply
Is there any special type of supply that connect mains or earth in the
  smallest possible way? How would it be named?


You can use a piezo electric transformer like this one by TI (formerly a Nat semi design): -



Disregard the lower half of the circuit because that is for a high isolation amplifier.

This overcomes the problem of capacitive coupling between primary and secondary producing mains voltages at your output terminals although you still have to be aware that any floating node will capacitively couple to your AC supply voltages. However, I expect this to be an order of magnitude (or more) down on conventional SMPS units.

Here's the link to the TI data sheet/article how to build one.

Another way is to use RFID technology with tuned primary and secondary coils spaced a centimetre apart to substantially reduce coupled capacitance to the power source.