I am commuting a similar distance at the moment, so have the same need to clean up. The shop I'm working at does not have a shower, so I do the sink routine. I pack a small toiletries kit, a washcloth and a small towel, and clean up with soap and water before getting into clean clothes. Since I work at a bike shop, it is easier than when I worked in the corporate environment - more casual clothes, mainly, so easier to pack things into the panniers.