Just played this great game (on easy) and we came across the situation several times where we had no aliens on the board but still wanted to do stuff. Can you just pick up the skull dice or do you have to sit there doing nothing for the rest of the turn because you have to action the skull before your next action and there are no aliens to move?
For maximum fun we just picked up the die ("moved" the non-existent alien) and continued rolling.
You were right. You just have to pick up the die and continue. Basically, this is one of the best things that can happen to your team: to have eliminated the aliens and still have time to roll the dice frantically to do whatever you want!