Aloha!
I remember a professor in a class I was taking in college telling us that the reason original Johnson's Baby Shampoo didn't sting eyes was because it contained a small amount of Novocaine to numb the eyes and thus, no stinging. Of course, this was false, but that was WAY before the internet was available for vetting such information and therefore many urban legends found their way into false information sources. Even colleges. Sad but true.
Anyway, I never tried Baby Shampoo as a preshave. This may not be popular with the masses, but I stick with Proraso Pre Shave Cream, even though it's more expensive than Noxema. It works, and I like the brand. I don't always use it, but when I do, I enjoy the extra protection it seems to offer.