If you can get a rack on your bike, I second using a pannier. It's amazing hoe much cooler/less sweaty you'll be with the pack off your back.
How about anti-bacterial wet wipes? I have some Nuetrogena (sp?) sunscreen that is fragrance free, but it's kind of thick.
This time of year, even when I do a 10 min. errand, I still think I smell. I don't seem to lose that smell until late October.