Here's a pic of some silicon being brushed into the mould to create a skin. I used Mouldlife Tinsil Gel 10 for this, combined with a thixotropic additive to thicken it up so I could brush it into the mould.
I've embedded the eyes of the puppet in the silicon here.
I repeated the same process for the back of the mould then put them together while they were still wet so that they joined together. Here's a pic of the completed cast with a fibre glass support inside to keep the silicon rigid.
Here's the completed cast. As I used a tin based silicon, air bubbles and seem lines can be filled in using silicon bathroom sealant.