Once chilled you can go right into cutting out the shapes. Once you have cut out all your shapes, bring the remaining dough back together and roll out again.
If you don't like the idea of using raw eggs in the icing, you can buy Royal Icing Mix that contains pasteurized egg powder - you just add water and mix in the Thermomix for a couple of minutes.
Once you have made the icing, transfer it immediately to a piping bag. It will start to dry out and thicken if you leave it in the Thermomix bowl too long. So transfer to the piping bag as soon as possible. If it thickens you can add a drop of water.