I only regularly put sunblock on my nose and the back of my neck, maybe a little across my cheekbones and ears. Badger is based on olive oil and beeswax, so it's definitely possible that it would be too heavy to put on your arms or back if overheating is a problem for you. Is that why you were asking about putting it somewhere besides my face?
As for whitening... a little bit. According to their
FAQ, the zinc oxide particles in Badger sunblock are for the most part larger than what's technically considered nanoparticles, although there's some overlap in the 70-100 nm range. So it's definitely not like the old-style clown-nose zinc oxide preparations; I would say the appearance is more like wearing makeup that's a shade too light for my skin.
Also, poking around Badger's website, I see they now have an unscented version. Men may prefer this too. ;)