You can use the Knife Project tool, to cut a new edge loop.
It will perfectly follow the object's curvature.
- Add a plane and position it where you want the cut
- Select the plane first and then your object
- Go to edit mode and use Knife Project with Cut Through checked.
Note: The cut depends on your current view - front/side orthographic works best.
As Robin Betts kindly pointed out, it's better to put the cutting geometry outside of the object, which allows to cut multiple edges at once.
Projector parallel to viewing plane...
Here, a grid with its faces (only) deleted
.. so multiple edges cut simultaneously.