I keep my work clothes and a dry towel at work. When I arrive, I wipe myself down with the towel, run a few scented Wet Wipes over my neck, chest, underarms, etc., apply deodorant, and change into my work clothes. For when the hair is too grungy looking, I keep a dryer on site.

It's very easy to use the "I need to look presentable" excuse to cop out of riding to work. I'm guilty of it myself, though less and less often. Try the ideas above. Heck, if you work in a supermarket, there must be PLENTY of products you can spray yourself with to eliminate the stink!