One way of looking at things that has helped some people, is to think of the energy needed for a day at WDW like a checking account. Each day, you get a certain amount of energy put into your "account" and as the day goes on, you "spend" energy at various things.
You can choose to use your energy for fun things, like going on rides, or for just basic activitites (like walking around the parks). You can conserve energy (and maybe even add to your energy account) by doing things like using an ecv or wheelchair or taking a rest. If you use too much energy during the day, you might not have enough to last the whole day. If you use too much and keep pushing anyway, you will "overspend" your account and begin the next day with a smaller amount. So, using an ecv or wheelchair is a sensible way to stretch your energy and help your whole family have a better time.
My FIL has been seriously talking about using an ecv at WDW for the past 6 or 7 years. He finally rented one the last day of our recent trip. He said it was wonderful and he wished he had done it years ago. He was able to go where he wanted and not have to think about how much he would "pay" for it later. It was the first time in years that he left a park without severe knee and hip pain. It was also a visit where we didn't have to say "I wish grandpa was here" or watch him be in pain. Hopefully, he will remember how nice it was and on his next trip, rent one earlier!
I'd feel a bit awkward walking up to Guest Services and saying "ahem...I know I don't LOOK sick, but I'm being treated for cancer and was wondering what you folks might be able to do for me?"
My understanding is that doctors notes are *not* needed...it wouldn't be a problem getting one tho...
To add a little to what the other posters wrote.
If you are using a wheelchair or ecv, you don't need a GAC to bring the ecv/wheelchair into line with you or use the accessible lines/entrances (most line are accessible).
If you have additional needs besides needing an accessible line, then a GAC might be helpful.
You don't need a doctor's note to request a GAC.
You do need to be able to explain your needs to the CM. Telling the CM you have cancer or another other condition doesn't tell them what your needs are because each person has their own needs.
For example, my DD has cerebral palsy and drives a power wheelchair. Several of her friends also have cerebral palsy and drive power wheelchairs, but they don't all have the same needs. One of the young ladies would have no problem driving her wheelchair in lines and could probably do well without a GAC. Another drives her wheelchair with something called a head array (she basically drives with her head). Some of the regular lines would be too tight and winding for her to drive in; besides, when she gets excited, her arms and legs fly all over and she would not be able to drive in narrower places without banging her arms on the rails. My DD would be able to drive her power wheelchair in many of the regular lines, but she has a lot of obsessive behaviors that make it difficult for her to be in line with a lot of people. So, just knowing a diagnosis, doesn't tell what the needs are at all.
So my advice is the same as the other posters. Rent an ecv and your whole family will have a better trip.