Hello Unk.
Skinning with synthetics is a delicate and precise process, that requires specific (and very expensive) tools and a vast amount of knowledge for you to achieve the precise tone.
Furthermore, even if you do master the techniques (spending time and money on Shamisen education in Japan), and invest several thousand USD in the tooling, I don’t think you will find only the skin readily available for sale, especially synthetics of any kind, unless you have a relationship with a Japanese Luthier.
For anyone not thinking about starting a Shamisen business, the best way to get a beautifully sounding skin on your Shamisen is to send it to Kyle in the US, or to their partner in Japan to have it skinned. The cost is not that high ($200~250) plus shipping back and forth.
An alternative, if you are OK with animal skin, is to buy cheap Goat Skin, give it the proper treatment, invest about $100 in DIYing a set of traditional Kawahari tools, and invest some time to acquire the knowledge.
This is not meant to discourage you, but skinning a Shamisen is not, by a long stretch, as simple as you think.
I wish you the best of luck.