First, there is no such thing as Chiropracty, Chiropractory, Chiropathy, etc. Now, there IS a degree called Dr. of Chiropody, but that's a foot doctor (chiropodist), and because of the confusion, they no longer use that term. (When I graduated from Chiropractic College, my grandmother asked me to cut her toenails. And no, I refused to do it.) This is the kind of thing that explains why we now know Chiropodists as Podiatrists, and Chiropractors have an uphill battle keeping their titles spelled correctly.
We who hold the D.C. (Doctor of Chiropractic) degree are CHIROPRACTORS, and we practice CHIROPRACTIC. That's it. There are no alternative spellings, no other terms used. And no, we are not "CHOIR" Practors, either. (One year, I sent out Christmas cards with a church choir on the front of the card. Inside it said, 'Merry Christmas from your Choir Practor.' I'm sure not everyone got the joke.)
Increasingly, however, our profession does use the term, Chiropractic Physician. Technically, that's not quite right either, but on the other technical hand, it is more correct than the other ridiculous-sounding names.
It's such a simple matter to use a dictionary and is one method I highly recommend when someone needs to use a term they may not be very familiar with... even if they just think they are.