Bizarrely, this is a situation that I've actually given a lot of thought to over the years. Three of my first cousins are genetically closer to me than the rest are (our fathers were brothers and our mothers were sisters, so we share two sets of grandparents) and we've not spoken to one another for almost twenty years, now. So I've wondered what I'd say if they needed any part of my body, quite frankly, including bone marrow and/or blood. I've wondered whether I would donate and then never speak to any of them again... or whether I would, essentially, leave them to try and find someone else to donate.
Like others, I'd not want to donate anything that my own children might, one day, need in some capacity. But I know that I'd come under a lot of pressure from other family members (I still have contact with their mother, my aunt, for example, and her younger children) to help/save them. Would they do likewise if I or my children ever needed something from them...? No. They wouldn't. I'm under no illusions regarding that (one of them actually threatened my life if I went to our Gran's funeral, so...).
So my answer would be a resounding "no".
And I wouldn't experience any guilt over that, either. Because it would simply be Kismet. A consequence of the choice which they made to make vile threats and act like the bullies they actually are towards everyone at a time when our family should have been pulling together.
If your nan is a bitch to you, OP, and you don't want to be tested/lose a kidney... then don't. There is no law that says you have to give any part of yourself to anyone else, for any reason! Your body = your choice. Please don't let your aunt, or anyone else, try to pressure you into doing something that you don't want. Understandably they're frightened about the consequences of her bitchiness, but... donation comes with its own set of risks to the donar. A lot of people don't stop to think about the donation part of it and what that will mean, forever, to the donar. They only think of the person who needs the donation...