I've used Pré de Provence and Organic Essence brand shea butters. They both have a very slight scent, kind of a lard-ish smell. If you put your nose right in the tub, the smell is distinct, but I would never notice it from farther away, in the quantities that I use it. Certainly not among all the other aromas of long distance cycling.

There might be a little bit of whitish residue that doesn't always come out of my chamois in Ohio, but my tap water is very cold. It seems to come out completely in Florida where the tap water is closer to 70°F. It's no more residue than I've experienced with any other lubricant that actually, you know, works rather than dissolving in my sweat. I figure that anything water-soluble comes out in the wash and any part of the shea butter that isn't water-soluble won't hurt me, particularly since I dry my shorts in the sun (probably not the best thing for the fabric, but one of my few concessions to modern bacteriophobia).