I'm not familiar with how SolidWorks Simulation handles hyperelastic material models, but I believe that you will need better data than you have in your data sheet. You need to send a suitable sample of the material to a materials testing laboratory where they can do the specialized testing to get the material data needed to set the material parameters in any of the hyperelastic models. Axel Products, Inc. is one we have used. It typically costs about $1000, although that was a numbe of years ago. They have a program where you can take a class and test your own material. That seems like a really good idea.
Blatz-Ko may be a good model. You won't know until you try to fit the data.