Just a thought: since your son is about 30 months old, and you've been on your own since he was 10 months old, that's 20 months. I'm assuming that that last day of custody court was something less than 20 months ago.
In terms of illness, that's not a very long time. What I'm suggesting is the possibility that your child's father, who now is at stage 4 of his illness, was beginning to be ill at the time that he left, and during the time that he did not respond to your emails?
I certainly am no cancer expert, and I've heard that some people can develop cancer quickly, and it proceeds at an excruciatingly quick pace, but many people begin to show less-dramatic symptoms early on, and their cancer develops more slowly. So is it possible that your child's father, over the last year and a half, perhaps was experiencing some symptoms of brain cancer, such as having difficulty reading, using a keyboard, speaking, or trouble with balance, for example?
Maybe that's why he resisted visits and communication? Could he have been incapable of visits, or perhaps embarrassed about his physical condition, or denying it?
I sympathize with your imminent loss, even if things were difficult between you and him. I'm sorry you have to make this decision on behalf of your son.
But if it were me, I'd reach out. I'd make the effort to see him, or his parents or sister or best friend or whomever. I'd try to get a photo of him and his son. When your son is older, you can truthfully tell him that his daddy was very sick and died (or went to heaven, or is with the angels, or has passed away or however your counselor or pastor or priest or friend helps you explain it). Someday, when your son is much older, you can choose to tell him more about your relationship with his dad, when he gets to the age when he's dating and thinking about starting his own family, or you can choose not to. That's up to you.
But for now, there is a very ill person who helped to create this little boy whom you love, and he may not be able to make good decisions (and maybe has not for some time) and perhaps one visit or one photo for your son will help your son in the future. If your child's father is too ill for a visit from a child, maybe you can visit and ask for a photo or a letter from either him or his family.