I have managed with one pair of shorts or sometimes two depending on the trip, but mostly one these days.
Rinsing or washing shorts out at night sometimes means putting them on damp in the morning. Some folks say that results in chafing for them but I have not found it to be a problem.
To be honest I usually wash shorts only every few days. Again some folks say that is a problem and they suffer rashes or saddle sores from that, but I have not found it to be a problem for me even on multi week trips. I do find that getting out of my bike shorts in camp and overnight to "air out" is important. I carry a pair of running shorts for that.
Oh and I do not use any chamois butter, but if I get any sign of irritation I apply some Balmex or other zinc based diaper cream overnight. It works like magic and by morning any irritation is gone.