go into all your lights, and in the little panel where you turn the shadows on or off, you'll see an "exclude" button. push that, then you'll see where you can tell the lights to NOT illuminate whatever you want. just go around to all your lights and pick the sky dome.
but, keep in mind, you will then have to set up some lights that ONLY light the skydome. go into the same "exclude" button on these lights, change it from exclude to include, and only pick the skydome.
easy as pie.