To accurately account for how the object feels when rotated through more than one axis (e.g., a turn of the wrist will feel different than swinging with the arm), you will also need the full inertia tensor. This can be fully specified by three numbers, the moments of inertia about the principal axes, instead of just one number for the moment of inertia you were considering in your question.

You will also likely wish to specify the vector displacement of the center of mass of the virtual sword with respect to the location the controller is gripped, so that you can determine the amount of rotation about each axis through the center of mass for any given motion trajectory

To accurately account for how the object feels when rotated through more than one axis (e.g., a turn of the wrist will feel different than swinging with the arm), you will also need the full inertia tensor. This can be fully specified by three numbers, the moments of inertia about the principal axes, instead of just one number for the moment of inertia you were considering in your question.

You will also need to specify the vector displacement of the center of mass of the virtual sword with respect to the location the controller is gripped, and the orientation of the principal axes, so that you can determine the amount of rotation about each axis through the center of mass for any given motion trajectory