Shaft material does make a difference. But in the real world most boats of similar size have similar engines and with a limited number of available sizes it doesn’t vary much. But it will matter in some cases. By the way its stiffness not strength that makes the difference.
The rigging size is also tied to clevis pin diameter so if you change to a stronger stainless you will probably stay with the same diameter anyway because changing diameter forces you to change tangs and chainplates. Changing stainless really just adds to the safety factor and nothing else.
All the best,