The N-634 doesn’t go to Avilés, it goes east-west. There is a road that connects Oviedo and Avilés, the AS-17, but it is a narrow, shoulderless, dangerous walk. The first time I walked from Oviedo to Avilés, I didn’t use GPS, and the arrows were bad. At some point after a town with a library (where we went for help, but no one had ever heard of the Camino at this spot), we wound up on that road, and it was very dangerous.
Since then, the marking has improved and I have GPS on my phone, so I have had two much more pleasant walks from Oviedo into Avilés. No industry, very rural.
The wikiloc tracks I’m pasting in are from a very reliable Wikiloc member, twin.astir. I would follow these tracks.
Camino de Santiago del Norte - Etapa 15: Oviedo-Avilés Hiking trail in Oviedo, Asturias (España). Download its GPS track and follow the itinerary on a map.
Camino de Santiago del Norte - Etapa 15: Oviedo - Avilés. Salimos desde la plaza de la Catedral. Cruzamos la calle Jovellanos, bajamos...