I just bought a switching power supply which is supposed to be connected to the power grid using three connections (Neutral, Live and Ground). Unfortunately, all common cables can be plugged into outlets in any rotation, which means that I don't always know where Neutral or Live is. Does this imply that I can only hard-wire the power supply and that I can't use a standard cable?
No. The power-supply does not require correct 'polarity'1 as it is insulated from ground and the datasheet (for which you didn't supply a link!) should indicate that the output is isolated from the mains.
Figure 1. A typical SMPS block diagram. Note the transformer provides isolation between the high-voltage and low-voltage sides of the circuit. Note also the isolation - usually optical - in the feedback circuit. The source of this image is lost, I'm afraid.
The one advantage of getting the polarity right is that the internal fuse in your supply will be on the 'L' line and if that blows it disconnects the rest of the circuitry from the live wire.
One of the advantages of the British 13 A plugs (also used in Ireland where I am) is that the polarity is guaranteed provided they are wired correctly.
1 I know, I know! Polarity is not the correct term for an alternating supply since it changes fifty times per second in Europe.