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Recent observations by the Event Horizon Telescope (EHT) indicate that the shadow of the compact object at our Galaxy's center (Sgr A*) closely resembles that of a Schwarzschild black hole. However, identifying the presence and exact location of unstable circular null geodesics outside the compact object (hereafter referred to as an exterior exterior photon sphere) observationally remains challenging. Motivated by this, we investigate shadow formation in spacetimes that lack an exterior photon sphere by applying the Simpson─Visser (SV) regularization technique (originally designed to smooth black hole singularities) to null singularity and charged null singularity metrics. We show that the regularized null and charged null singularity spacetimes exhibit shadow-like features despite the absence of an exterior exterior photon sphere. We analyze how the SV regularization parameter influences their geometry and shadow size, and show that the regularized null and charged null singularity spacetimes can correspond either to two-way traversable wormholes or retain singularities. For the wormhole branch, the spacetime admits an unstable null orbit at the throat while remaining free of an exterior exterior photon sphere. Apart from the shadow-like dark region without an exterior photon sphere in the charged SV spacetime, our investigation shows that, for a specific range of parameters, the shadow boundary (dark region) is controlled by the regular core rather than by an exterior photon sphere. Our results reveal that shadows arising from these regularized null singularity spacetimes closely mimic those of Schwarzschild and charged black-bounce spacetimes, even though no exterior exterior photon sphere exists. We also perform a phenomenological comparison of the predicted shadow sizes with the EHT observations of Sgr A* and M87, identifying parameter ranges compatible with the observed angular diameters.