SkinStudio is not part of the WindowBlinds install, which is why clicking edit on a style sends you off to the product page. There is nothing on your machine for it to open yet.
You do not need Object Desktop to get it. It is a separate download either way, and the current one is public:
https://cdn.stardock.us/downloads/public/software/skinstudio/SkinStudio_11_setup.exe?a=sd
If you do happen to have an Object Desktop subscription it also appears in Object Desktop Manager, so that route exists as well. It is just not the only one.
The part that matters for you is the licence. Our SkinStudio page says a valid WindowBlinds licence is required to use it, and the standalone download will not function without WindowBlinds installed. I am not going to tell you a trial definitely satisfies that, because the wording does not say either way, but the installer costs nothing so it is worth finding out.
One thing worth knowing before you go down that road: if you only want to change an existing style rather than build one from scratch, WindowBlinds can modify a skin from inside the app itself, including applying your own texture to one of the bundled ones. That may be all you need.