Honestly, I really wouldn't worry. I had a baby last year and had four indoor cats, two of whom were elderly. None had had any contact with children or babies. ( Tho they had been used to new cats arriving ).
If you are calm and chilled, chances are your baby will be, and heshe might not even be a screamer, not all of them are.
I adapted a travel cot so the cats could remain sleeping with us. I'll tell you how if you are interested, it was very easy. I didn't go down the Moses Basket route because I'm aesthetically allergic to wicker.
I had no problems, but assumed I would have no problems, and I don't know if that helped but think it might have done.
One thing I did do was let the cats have a lot of contact with the baby, baby on knee, cat on knee. I was in hospital for a bit after giving birth and I sent babygros home so they could get a good sniff of her.
Make sure your health visitor isn't allergic to cats or is intelligence deprived when it comes to babies and cats.