Lucy Took said (in a pm, since she was in a nice mood) she was at a Lutheran College and was lost with my Catholic Terminology.
There is one thing Baptists and Lutherans have in common. They think Adam's sin remains after baptism.
We Catholics think it leaves residues after baptism. The "law of sin in the limbs" is this kind of residues, but is, after baptism, not a sin in itself, it is just coming from sin and giving occasion for sins. Personal ones.
So much on original sin/Adam's sin.
Now, for the practical problem. The uncle is, I take it, still alive.
That means he can still be baptised and saved.
Normally children cannot be baptised against the will of parents or those who are legitimately in their place. There is an exception when a child is in danger of death. Now, part of the reason for the main rule is that children usually grow up and can later decide to be baptised if parents didn't want it for them.
I don't know what to think of this uncle, if it is just a question of cerebral paresis, this should not prohibit him from an adult understanding of what is involved, though it may impede the physical act of expressing it (Stephen Hawking is communicating through one muscle).
But if it is sth like Downs, too, then he will normally speaking never grow up, and others than he would have to take the decision for baptism.