I checked the printed list (citation below) for your Conrad Ochs or Axe and there is no one by that name. There is a Johannes Ochse, so you might want to add that spelling variation to your searches.
Barth, Richard C., William E. Dornemann, and Mark A. Schwalm. "The Trenton Prisoner List." Journal of the Johannes Schwalm Historical Association 3 (1985):1-21.
An answer to this other g2g on the Hessians includes a link to a German website with a search engine for Hessian Troops in America; still no Conrad listed.
You will not find every Hessian service member on the Trenton prisoner list. The estimate is about 30,000 Germans (mostly Hessians) served England, but only about 1,000 were captured at Trenton.
Here are some research strategies for researching Hessians in the Revolutionary United States from the library that holds the Schwalm Association records (they don't provide direct research assistance, however).