If the shower is that important, stay at hotels/B&Bs and regular campsites that have showers. If that's not available, you can clean yourself very well with a small bottle of water and a little soap, or baby wipes. I take a shower after arriving at the destination, to get rid of dirt and sunscreen, helps keeping the inside of the tent and sleeping bag clean.
I can wear the jersey and socks the second day, if I have to, but not shorts. That's just gross. I have to have clean shorts.