As a cat owner who has cats that have not shown any attempt to sleep with either baby, I would love to know of any actual cases of cat suffocation. I find whilst my cats love to sleep in any bed, once they work out a baby is there, they jump out very quickly all without any training from us. I have heard to be careful with cats, but honestly have never come across any news article or verifiable incident where a baby has died due to a cat.
I agree with Astrid,
I'm yet to hear of a cat suffocation, my cats always disappeared when bub's was around. A girlfriend of mine bought a mosquito net and use to put that on her cot just to give the cats the idea that the cot was a no go area!
Good Luck with it, I wouldn't be going to the extent of a screen door tho!