How to render a real wireframe:
1. Select all of you model geometry.
2. Press Ctrl + V.
3. Make a copy.
4. Whilst still having the copied geometry selected apply the push modifier.
5. Set the value to 0.1
6. Open material editor and apply a new material onto the geometry (Apply to selection if it asks).
7. Change the new material colour to black, and check the "Wire" checkbox.

Do that please.