I walked the Camino for my grandson, who had been battling cancer for a year when I left. He had finished his chemo and radiation therapy before I planned for and began the CF, and we thought he was going to be okay, but it was a very bad kind of cancer and there was a substantial chance of it recurring. A month after I returned, his cancer came back and he died two months after i got back.
I left so many prayers, and tears, in so many churches and paths and pillows along the way. I told his story and showed his picture to pilgrims along the way, and asked them to carry his name with them, and they told me they did. I bonded deeply with so many people in my sweet grandchild's name... it was pretty amazing.
So I would say that you can most definitely walk the Camino for your friend, and you will be doing it for yourself, and for all those you meet that you tell about him, and of course also for him. But I wouldn't worry at all about the Compostela. He is going where he can't take it with him. Write your journey for him in the compostela of your heart, dedicate it to him there, that is the real place to keep it.
Also, since my pilgrimage was such a single-minded and fervent prayer for our Little Bhau, I made the decision not to take a camera, as it was far from that sort of trip for me, and to try to accept whatever happened along the way with grace in honor of his suffering. Both of these stood me in good stead along the Camino.
lots of love and good wishes to you on your Way!