Based on this guide, using Vreeberg's TPE film, and PFS-300.
I tried to cut one pocket and make a small balloon for this puppet. I used the 25cm gathered fabric type II (Emmi's marking). The stretch was just not enough to get a significant bend. I pumped more and more pressure and eventually the balloon managed to rip the seam!
I could still try one of the more stretchy or longer gathered pockets to see if they are better, but for now I am OK with using the bigger squirrel puppet and longer pocket.