my opinion is that there is no material model better than others in reproducing an unknown behaviour. In other words, in your situations I would struggle to suggest any material model capable of giving you a better fit over arbitrary deformation modes, etc. by simply knowing an engineering tensile stress-strain curve.
In order to maximise my chances I would try to choose a model with some physical foundations. It also depends on the type of rubber: for example, if I remember correctly using 2 coefficients-Mooney Rivlin systematically overestimates the stiffness in biaxial modes for SBR, heavily flled, rubbers.
If your analyses does not involve excessively large strains, if the prevailing deformation mode is tensile, if there is not very pronounced volumetric/deviatoric coupling, maybe you could get away with it. I would take example from the great physicists of the past, who, whenever anything is unknown, postulated it to be constant or linear. I would then choose a Neo-Hookean and see where I get to.
Let us know!
Thanks a lot Muzialis