My grandmother is also struggling with cancer and in her case she is "afraid" and we are in similar situation with her obsessing and being scared when and if people find out she has cancer.At first I couldnt grasp my mind and understand how is that even fucking possible, but I realized its just cultural/generational thing.In her relatives/friends group(which are pretty old) cancer is instantly linked with death since when they were young they didnt even know it exists and growing up they only hear that someone passed away from it, so she is always worried if people find out, what would they say, if people can tell shes wearing a wig etc... which takes a mental toll on her and it really pisses me off.She even rushes to the car using all her strenght so "people dont see her" and there is simply nothing we can do to change that.After a while she got a bit loose and relaxed, but she still worries about dumb shit like that for absolutely no reason.

So I would say if its that much of an issue for your father and causes him mental toll, he has simply grown up like that and those things matter to him and theres no convincing otherwise if it pisses both of you off and your family just go and do it. Its probably some stupid ceremony anyway and it will probably only make him feel better if only for a while.

The whole situation is anxious and scary for all of us and honestly we have no clue whats happening most of the time but least we can do is be there for eachother and support eachother, if that means some stupid ceremony then so be it, dont think of it as "public humiliation" but you spending some time with your father and do what he wants.

In grand scheme of things, everyone is scared and dont believe for a second anyone is blaming you for anything that is the worst thing you can do to yourself and the people around you.

I say if it means that much to him just go and do it and dont overthink it like its something special good or bad, its just some tradition that your father does/likes and I hope and wish for a smooth and speedy treatment.