The sentiment is more important than the ring itself right now. He could present it to her as is, pop the question, and then take her and it to get the ring resized, reset, or whatever she prefers! I am sure she will be touched that it was his grandmother's ring.

I speak from experience. My wedding ring was Paul's grandmother's. When I first saw it - opposite problem - it was so big it fit on the knuckle at the base of my thumb. My mum-in-law has suggested to Paul that I just get the stones reset to something modern, but I loved it as is. And wear it to this day, once it was resized to fit my ring finger!