Start by cutting out a cross of chicken wire in the desired size. (E.g.: 17cm per later side)
Bend the sides down.
You should end up with a cube with an open bottom.
Fixate the cube with the zip ties.
Attach the fairy lights with the same method. Make sure to distribute them evenly but with enough variation.
Cut out a cross of thick translucent paper.
Wrap it around the wire cube but make sure nothing overlaps.
Cut a whole into the bottom.
Wrap it in washi paper like a normal present but leave the fold at the bottom open, so that you can access the battery pack.
Add a nice ribbon.
Packages of different sizes look nice next to each other (when finished ;-) ).