LED lights use very small amounts of power usually (but then they're not usually very bright either). What this means is that you can probably leave the mains power supply on all the time, and just swich the low voltage wires to the LED itself. In fact, both the ones I bought have exactly that sort of switch.
The polarity of the power cable from the 'wall-wart' to the actual LED matters. Unlike ordinary light bulbs and CFL bulbs, LEDs actually use DC*, so you'll find the plugs can't be reversed - the Ikea ones seem to use a blade and pin design for this reason. As long as you keep the polarity correct (be careful with this), you can extend the cables to the wall adaptor, or shorten them as necessary.
*They will work on AC, sort-of (LOW voltage, not mains!), but they only come on for half the time, and flicker at 50Hz. Most people find this more annoying than fluorescent tubes because fluorescents flicker at twice the mains frequency (i.e. at 100Hz), and the way they are constructed tends to mimise the effect too, whereas it's very obvious with LEDs. LEDs can't be usefully dimmed either, without a complex circuit.