Be creative. As a paying customer, there are enough publicly accessible places in SdC you can do a quick wardrobe change, and give yourself a quick and discreet 'bird bath' in a wash hand basin to freshen up enough to be squez against other...
I noticed at Albergue Fin del Camino they charge €5 for a shower if you are not staying the night. But ring them, because they often have school groups staying and are closed to other pilgrims then
There is a public bathroom as you face the cathedral behind you to the right down the steps and against the wall there. There are two or three restaurants with tables along that area so look along the wall for the doors.
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