We introduce the first variance-aware algorithms for contextual dueling bandits that leverage shallow exploration strategies with neural networks for nonlinear utility approximation. A key theoretical challenge is the absence of a closed-form estimator, which led prior work to require an extremely large network width $m$ (i.e., $m = \widetildeΩ(T^{14})$). We address this constraint with a novel analytical approach that combines iterative self-improvement with spectral analysis. Our analysis significantly reduces the network width requirement to $m = \widetildeΩ(T^{6})$, and shows that our algorithms achieve a sublinear regret of $\widetilde{\mathcal{O}}(d\sqrt{\sum_{t=1}^{T} σ_t^2} + \sqrt{dT})$ under both UCB and TS frameworks. Empirical results show that the proposed algorithms are not only computationally efficient and exhibit sublinear regret in practical settings, but also achieve state-of-the-art performance on both synthetic and real-world tasks.