You can spray Viper inside the home, leave for at least an hour (along with the cat) until the product is dry, then it will be safe to return for humans and animals.
Saying that, however, I would not use this product for spiders.  Demon WP is the product you are wanting to get rid of spiders, which is a wettable powder that can be made into a spray.  The same precautions apply as with Viper for leaving the house after spraying.
If it is not possible to leave the house, then I would suggest getting Big H Brown Recluse Spider Traps
You can put these in out of the way places so that the cat cannot get to them. Mine catch other insects besides all types of spiders.