Well...That depends on how 'non-traditional' you mean. If it means not having taken a single physics or science course at the college-level, your chances are virtually non-existent. The kinds of non-research jobs available include manuscript editor, planetarium guide, museum guide, telescope operator but even these require some background in astronomy and physics. Most require that you have at least a BA or Masters degree in astronomy. With the job situation in PhD-level astronomy being what it is, there is now a pool of young astronomers willing to consider some of these kinds of jobs for themselves, so there is quite a pool of talent for prospective employers to look through.
You might consider writing books or articles, but there you may not find much of a career especially if you freelance.
The bottom line is that finding astronomy-related work is very hard. It isn't always a 'given' that one can turn a hobby or intellectual enthusiasm into a career. Astronomy is such a small career ( 6000 people nation wide) that it is probably one of the worst in which to find a broad range of available jobs. Still, some things are best left as a lifelong interest rather than a career. Astronomy is certainly one of the most active 'hobbies' in the world! Good luck, and keep in touch!