I respectfully suggest that you bring a smart phone, fully charged, and turned off if you insist. BUT, it is far better to have it and not need it, or choose not to use it, than to find yourself in a difficult or emergency situation, without a means to call for help. Make sure you have pre-loaded the necessary apps to help you - just in case. Alert Cops is one such app that we in the forum highly recommend.
While I fully understand the desire to be truly disconnected, be aware that this "freedom" has definite drawbacks. In my 70+ years experience on this mortal coil - 11+ as a pilgrim, I have long ago learned that as soon as I let down my guard - like not bringing an emergency means of summoning help, something will happen to make me regret that decision. The modern smart phone is like a digital data Swiss Army Knife. You literally have the knowledge of the world at your fingertips. But, as I said, I respect your choice.
Still and all, it IS your Camino and you may accomplish it however you think best for you. If you do not bring a smart phone for summoning or locating help while on your Camino, I recommend that you carry an ICE (In Case of Emergency) document printed and in a waterproof bag.
Consider keeping it with your national passport. This way, if someone finds you incapacitated or worse, they know what your medical needs are, and who to contact in am emergency. This is especially true if you have a chronic condition, or must take prescription medication regularly.
I have carried one one on every Camino since 2013. It is translated into three languages: Portuguese, Spanish and French - plus English. So, even with a functioning smart phone, if someone comes upon my unconscious - or worse - body - the appropriate assistance can be summoned. I owe my family and loved ones at least that much.
Hope this helps.
Tom