Owning a pet doesn't have an impact on an appraisal, in and of itself. However, the condition of the home is factored in, and only if the pets have caused damage to the property will the appraisded value be affected.
Best of luck
But removing your cats for every showing is a bit over the top - and could be mighty upsetting for the cats. If there is a risk that they will bite or scratch a visitor, then that's another matter. But if not, then just make it clear in the agent remarks that you have cats - perhaps "please be careful that cats don't get out..." whatever you'd like to communicate.
But let me move on from the cat question and congratulate you on securing relo benefits as a part of your job tranistion - GREAT! - that will really help to ease what can be a stressful process.
Good luck to you!
Unwavering Commitment to Service
Once you get ready to show your house, hide all evidence of your pets for any showings. I actually will take the cats out of the house for showings during showings! Certainly dogs must not be present (even in the garage) during showings.
Good luck with your move.