Freelance astronaut! Start off by getting your own rocket, and build it by yourself. Get your handiness up and build an observatory too, (I know that's not currently in the game, but they could patch it in).
Freelance vet could work too. You make one of your house's rooms the place where you'll see your patients. You prepare it as a vet clinic, with all the objects that are necessary. Your patients can wait in the hall until it's their turn. And then you give them their medicine etc.
Freelance singer. You only go to auditions, like the acting career. You upgrade your skills by yourself, and then go to auditions for tv shows, competitions, concerts etc.