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The question you posed is a toughie.
It's difficult to answer your question because I'm not sure what your future goals are. Are you interested in becoming a classroom teacher or do you see yourself teaching dance?
You may want to visit one of the local universities or colleges in New York to talk to a guidance counselor. The counselor would have access to all of the information regarding program requirements and so forth.
If you're simply interested in teaching - New York is reputed to have a teacher shortage ... and if you had a college degree, you could get emergency certification and find yourself in a classroom even if you didn't have an education background. You could then teach and work towards certification.
The advantage to doing this is that you could get into the classroom sooner ... but the disadvantage is that you could conceiveably wind up over burdened - teaching by day and taking classes by night.
If you have the luxury of time and money, I'd go for the education degree ... but that's just me. I prefer taking on challenges one at a time.
If you talk to a school administrator, the principal might be able to put you in touch with one or more teachers on his or her staff who have emergency certification. You could then introduce yourself to these teachers and talk to them about their experiences to get a better idea of what would work out best for you.
Out of curiosity - how do you use dance to help engage students in the learning process without teaching dance technique?
Moderator for the New Teachers' Place @ Teacher Focus