Cats and a home birth?

We have two cats, they’re sisters and just about two years old. They’re really good cats, very chill and good listeners. They’re both pretty used to being the centre of attention, and can get a little aggressive when they want you to pet them and you’re occupied with something else.

We’ve planned to have a water birth at home. Now, both of the cats seem to get pretty anxious whenever I am in the tub already (think constant meowing/whining), combine that with all of the things that happen with labour. I’m worried about them getting very stressed out, clawing at the inflatable tub, etc. Does anyone have experience with this? What did you do with your pets?