  A novel nonlocal four-photon interaction on the deformed spacetime is derived
and studied in the three selected models (I, II, III). The first two models (I,
II) are obtained via two distinct second-order $\theta$-exact Seiberg-Witten
maps of the noncommutative U(1) gauge field strength on Moyal space. The third
one (III), inspired by the manifestly gauge invariant structures emerging in
the first two, due to the model generality has been constructed with a
different set of freedom parameters. The physical relevancy of all models is
analyzed by evaluating the four-photon-tadpole diagram, which, when combined
with the bubble graph, enables us to fully consider all contributions to the
one-loop photon polarization tensor. For an arbitrary noncommutative matrix
theta^\mu\nu, the full quadratic IR divergence cancellation in the one-loop
photon two-point function is obtained with particular combinations of
Seiberg-Witten map/gauge-symmetry freedom parameters in models I and II.
Finally, our model III enables complete elimination of all pathological terms
in the photon polarization tensor at one-loop order if a special value for the
theta matrix is chosen.
