I don't want to sing at my great-uncle's funeral
Why do you want to back out from singing?
He was not that close to me.
You should be more respectful of the situation and sing at the funeral. Your family will be pleased and it is best to make your family happy during a sad time or they will be disappointed in your behavior.
I can't handle being responsible in that situation and I'll start a fight instead.
I think that you should still try to sing, I mean they asked you for a reason. It is expected that you honor your family's wishes at a funeral.