I used to have a cat that did EVERTYTHING with me. When I sewed he had gotten too big to hold so I rolled up the bottom of my shirt and pinned it like a baby carrier. He slept in there and I sewed and cut over top of him. Always careful to keep thread and pins away, etc. I carried him around that way to do all my household chores. I miss him dreadfully, but a great horned owl got him one night. That was years ago and we have moved and our present cat is not allowed in the work room. She is not even interested which is a good thing.
Enjoy your fur kids. They are worth it.