My cat also has a thing for rubber stuff and we have to keep rubber bands put away, we have seen them hanging out the other end with a 'small decoration' on them.
I would probably isolate the cat from the baby, we had a cat we had to put in the basement every night when it was small. But Oh I would not be able to live without the Binky!
And it is not physically possible for a cat to suck the air out of a baby, that is why they have to lap up drinks, they don't have a mouth that works that way.