Technical t-shirts seem to be a better solution than simple cotton t-shirts. They are lighter and dry much faster, 1-2 hours in summer, 3-4 hours otherwise. You should take only 2 of them for your Camino changing them day by day.
If you don’t want to wash your t-shirts every day, chose a merino wool t-shirt. This keeps you warm when it’s cold, and keeps you you cool when it’s hot. They dry in a flash and don’t stink.