You start in blender:
1. Open your animal's .blend file.
2. Click File > Export > NetImmerse/Gamebryo (.nif & .kf & .egm).
3. Browse for a place to export to. Click Export NIF/KF.
4. Click Zoo Tycoon 2 and make sure Export Skin Partition is on. Click Ok.
It goes on in Nifskope:
5. Open the exported .nif, right-click the model and click Block > Copy Branch.
6. Open the base animal's .nif file and find the NiBoneLODController by clicking the pluses. The NiBoneLODController is a child of the Bip01 node. Right-click the NiBoneLODController and click Block > Remove.
7. Now remove all nodes that contain LOD and/or the animals name by right-clicking them and click Block > Remove Branch.
8. Optional: Remove all stuff that somehow remained, which is directly below the Scene Root and thus parent-less.
9. Select the Scene Root, right-click it and click Block > Paste Branch.
10. Do the white animal fix. Save and Exit.