With all due respect, if used correctly in your bearings, and any excess external grease is cleaned up at each bearing service, your bike should never "ooze" grease onto the pavement. But even if your bike does drop a tiny grease glob along the way, does it really hurt anything other then possibly stain someone's nice white tennis shoes?

I personally don't believe it will. Here's why:
Crude oil, which is the basis for one of the primary ingredients (mineral oil) in "regular" grease, is a natural substance produced in the earth. There are all sorts of bacteria which live off of crude oil which comes to the surface either naturally or by human activity. The other primary ingredient is soap, which we all know is a cleaner. So between the bacteria and the soap, a little drop of grease here and there is quickly disposed of in a very natural way.
Synthetic grease substitutes vegetable oil for mineral oil. Pretty much anything living can consume vegetable oil with no effects, especially in the small doses inadvertently introduced by bicycle bearings. I'll admit soup can be hard to digest, if you try to eat a whole bar or drink the entire bottle of hand soap.

But in the small amounts we are talking about, I'm guessing even the smallest song bird would experience nothing more then a nice internal "cleansing."
So my advise is use the grease you think smells

the best. Clean off any and all external excess after servicing your bearings. And go enjoy the ride. Oh--- and don't forget you introduce carbon into the environment every time you exhale--- and all the plants love you for this!