I would suggest that you be very very very cautious indeed. The currents along the del Norte are pretty vicious-- a Guardia Civil whom I met on a beach when she was prepping for some surfing told me that she was in the Search and Rescue division or, she said, should be better called the Search and Recover Division. I have had a few swims on the del Norte at Islares west of Castro Urdiales, Playa Galizano (out of Guemes), in front of the village in La Isla, at Aguilar near Muros de Nalon, Meixota west of Tapia de Casariego, and de Arnao just before the bridge into Ribadeo, but at other places I would not have thought for a moment of doing more than a wade to my waist.
As a length swimmer at home, I was a bit frustrated by not being able to take a daily swim, but this is a coast where safety is a concern. Always check with the locals. As well, in May, the beaches are less likely to be lifeguarded. And always check with the locals.
The del Norte is a spectacular route-- pilgrims are not the only focus of the area as they are on the Francese, but with albergues, churches, and seafood, you should do all right.