After much thought, and after explaining to dear daughter that this hamster was about 100 human years old, couldn't be handled and might die at any moment, I decided to take her.
First I researched and read what I could find on hamster care, elderly hamsters, hamsters with eczema and allergic hamsters. I could see that I need to change her bedding (wood shavings baaaad), diet and environment.
She needs hypoallergenic bedding, hamster feed augmented with particular fruits and veggies, and a quiet, calm environment. No stress allowed!! Olive oil massages were also recommended, but I don't think so (the mental image of me massaging an old hamster with oil is haunting me).
Dear daughter and I have discovered that she loves a few paper towels to arrange into a nest and julienned carrots. She has quite a stash of sunflower seeds that she breaks out when no one is looking. And while she is quite feeble, she is still able to take care of her day to day basic needs.
Her name seems to be involving, but I am leaning towards "Grandpa". Dear daughter pointed out to me that dear hamster looks remarkably like my father did during the last year of his life. Sort of bald and wrinkled, but with a pleasant, serene expression. My dad had a great sense of humor and would have loved this.
So Grandpa has settled into a happy routine of sleeping, bathing herself, eating, chewing and you know what. I hope her last weeks or months of life are easy and pleasant.